EduSahara™ Assignment
Name : Trigonometry Miscellaneous
Chapter : Trigonometrical Identities
Grade : ICSE Grade X
License : Non Commercial Use
Question 1
1.
Which of the following are true?
a)
    • The value of
    •  
    • tan
      F
    • is always less than 1
b)
    • cos
      F
    • is the abbrieviation for
    •  
    • cosec
      F
c)
    • The value of
    •  
    • sin
      F
    • is always less than 1
d)
    • The value of
    •  
    • cot
      F
    • is always less than 1
e)
    • If
    •  
    • sin
      F
    • = 0 , then
    •  
    • cos
      F
    • = 1 or
    •  
    • cos
      F
    • = -1
  • (i)
    {b,e}
  • (ii)
    {a,c}
  • (iii)
    {c,e}
  • (iv)
    {d,a,c}
  • (v)
    {b,e,c}
Question 2
2.
For angle values from 0° to 90°, which of the following are true?
a)
The product of the sine and cosine values remains a constant
b)
The tangent value of the angle increases
c)
The cosine value of the angle increases
d)
The cotangent value of the angle increases
e)
The sum of the squares of the sine and cosine values remains a constant
f)
The sine value of the angle increases
  • (i)
    {c,b,e}
  • (ii)
    {d,a,f}
  • (iii)
    {b,e,f}
  • (iv)
    {c,e}
  • (v)
    {a,b}
Question 3
3.
    • Which of the following are true?
a)
    • The cotangent of an angle is the reciprocal of the tangent of the angle.
b)
    • sin
      (
      E
        +  
      F
      )
       = 
      sin
      E
        +  
      sin
      F
c)
    • The cosecant of an angle is the reciprocal of the secant of the angle
d)
    • cos
      (
      E
        +  
      F
      )
       = 
      cos
      E
        +  
      cos
      F
e)
    • The cosine value of an angle is the reciprocal of the sine of the angle.
f)
    • tan
      E
    • = tan
    • E
  • (i)
    {a}
  • (ii)
    {f,a}
  • (iii)
    {d,e,a}
  • (iv)
    {c,a}
  • (v)
    {b,a}
Question 4
4.
    • Which of the following are true?
a)
    • sin
      (
      G
        +  
      H
      )
       = 
      sin
      G
        +  
      sin
      H
b)
    • tan
      (
      G
        +  
      H
      )
       = 
      tan
      G
        +  
      tan
      H
c)
    • The value of
    • sin
      θ
    • increases as
    • θ
    • increases from
    • to
    • 90°
d)
    • The value of
    • cos
      θ
    • increases as
    • θ
    • increases from
    • to
    • 90°
e)
    • sin
      θ
       = 
      cos
      θ
    • for all
    • θ
f)
    • cos
      (
      G
        +  
      H
      )
       = 
      cos
      G
        +  
      cos
      H
g)
    • tan
      θ
       = 
      cot
      θ
    • for no value of
    • θ
  • (i)
    {f,c}
  • (ii)
    {c}
  • (iii)
    {b,c}
  • (iv)
    {a,c}
  • (v)
    {d,e,c}
Question 5
5.
    • If
    • sin
      2
      E
       = 
      2
      sin
      E
    • , then
    • E
    • =
  • (i)
    60°
  • (ii)
    45°
  • (iii)
    90°
  • (iv)
  • (v)
    30°
Question 6
6.
    • If
    •  
    • sin
      (
      D
        +  
      E
      )
    • =
    • 1

      2



      3
    •  
    • and
    •  
    • sin
      (
      D
         
      E
      )
    • =
    • 1

      2
    •  
    • ,
    • find
    • D
    • &
    • E
  • (i)
    D
    =
    43°
    ,
    E
    =
    13°
  • (ii)
    D
    =
    47°
    ,
    E
    =
    17°
  • (iii)
    D
    =
    44°
    ,
    E
    =
    14°
  • (iv)
    D
    =
    46°
    ,
    E
    =
    16°
  • (v)
    D
    =
    45°
    ,
    E
    =
    15°
Question 7
7.
    • If
    •  
    • tan
      (
      D
        +  
      E
      )
    • =



    • 3
    •  
    • and
    •  
    • tan
      (
      D
         
      E
      )
    • =



    • 1

      3
    •  
    • ,
    • find
    • D
    • &
    • E
  • (i)
    D
    =
    47°
    ,
    E
    =
    17°
  • (ii)
    D
    =
    43°
    ,
    E
    =
    13°
  • (iii)
    D
    =
    45°
    ,
    E
    =
    15°
  • (iv)
    D
    =
    44°
    ,
    E
    =
    14°
  • (v)
    D
    =
    46°
    ,
    E
    =
    16°
Question 8
8.
    • In
    •  
    • △HIJ
    • , right angled at
    •  
    • I
    • ,
    • if
    •  
    • tan
      H
    • =
    • 5

      9
    •  
    • ,
    • find
    •  
    • sin
      H
      cos
      J
        +  
      cos
      H
      sin
      J
  • (i)
    1

    5



    106
  • (ii)
    1
  • (iii)
    5

    106



    106
  • (iv)
    1

    9



    106
  • (v)
    9

    106



    106
Question 9
9.
    • In
    •  
    • △EFG
    • , right angled at
    •  
    • F
    • ,
    • if
    •  
    • tan
      E
    • =
    • 5

      8
    •  
    • ,
    • find
    •  
    • cos
      E
      cos
      G
         
      sin
      E
      sin
      G
  • (i)
    1

    8



    89
  • (ii)
    0
  • (iii)
    1

    5



    89
  • (iv)
    8

    89



    89
  • (v)
    5

    89



    89
Question 10
10.
    • If
    •  
    • cot
      θ
    • =
    •  
    • 1

      4
    • , find
    •  
    •  
       
      (
      1
        +  
      sin
      θ
      )
      (
      1
         
      sin
      θ
      )

       
       
      (
      1
         
      cos
      θ
      )
      (
      1
        +  
      cos
      θ
      )
  • (i)
    (
    -1

    16
    )
  • (ii)
    1

    18
  • (iii)
    3

    16
  • (iv)
    1

    16
  • (v)
    1

    14
Question 11
11.
    • If
    •  
    • tan
      θ
    • =
    •  
    • 5

      6
    • , find
    •  
    •  
       
      (
      1
        +  
      cos
      θ
      )
      (
      1
         
      cos
      θ
      )

       
       
      (
      1
        +  
      sin
      θ
      )
      (
      1
         
      sin
      θ
      )
  • (i)
    25

    36
  • (ii)
    23

    36
  • (iii)
    3

    4
  • (iv)
    25

    34
  • (v)
    25

    38
Question 12
12.
    • Find the value of
    •  
    •  
       
      (
      1
        +  
      sin
      θ
      )

       
       
      (
      cos
      θ
      )
        +  
       
       
      (
      cos
      θ
      )

       
       
      (
      1
        +  
      sin
      θ
      )
  • (i)
    2
    cos
    θ
  • (ii)
    2
    cosec
    θ
  • (iii)
    2
    sin
    θ
  • (iv)
    2
    sec
    θ
Question 13
13.
    • Find the value of
    •  
    • 7
      sec
      2
       
      θ
         
      7
      tan
      2
       
      θ
  • (i)
    0
  • (ii)
    1
  • (iii)
    7
  • (iv)
    10
  • (v)
    4
Question 14
14.
    • If
    •  
    • tan
      θ
        +  
      cot
      θ
       = 
      2
    •  
    • , find
    •  
       
      tan
      2
       
      θ
        +  
       
       
      cot
      2
       
      θ
  • (i)
    1
  • (ii)
    4
  • (iii)
    3
  • (iv)
    0
  • (v)
    2
Question 15
15.
    • If
    •  
    • tan
      θ
         
      cot
      θ
       = 
      7
    •  
    • , find
    •  
       
      tan
      2
       
      θ
        +  
       
       
      cot
      2
       
      θ
  • (i)
    52
  • (ii)
    50
  • (iii)
    51
  • (iv)
    49
  • (v)
    54
Question 16
16.
    • If
    •  
       
      sin
      6
      x
       = 
       
       
      cos
      (
      (
      x
      +
      34
      )
      )
    • , then
    • x
    • =
  • (i)
    8
  • (ii)
    9
  • (iii)
    10
  • (iv)
    5
  • (v)
    7
Question 17
17.
    • If
    •  
       
      cos
      7
      x
       = 
       
       
      sin
      (
      (
      x
      22
      )
      )
    • , then
    • x
    • =
  • (i)
    12
  • (ii)
    13
  • (iii)
    15
  • (iv)
    14
  • (v)
    16
Question 18
18.
    • If
    •  
       
      tan
      7
      x
       = 
       
       
      cot
      (
      (
      x
      6
      )
      )
    • , then
    • x
    • =
  • (i)
    15
  • (ii)
    12
  • (iii)
    13
  • (iv)
    9
  • (v)
    11
Question 19
19.
    • If
    •  
       
      cot
      6
      x
       = 
       
       
      tan
      (
      (
      x
      +
      27
      )
      )
    • , then
    • x
    • =
  • (i)
    10
  • (ii)
    7
  • (iii)
    8
  • (iv)
    12
  • (v)
    9
Question 20
20.
    • If
    •  
       
      sec
      8
      x
       = 
       
       
      cosec
      (
      (
      x
      9
      )
      )
    • , then
    • x
    • =
  • (i)
    10
  • (ii)
    11
  • (iii)
    13
  • (iv)
    12
  • (v)
    8
Question 21
21.
    • If
    •  
       
      cosec
      8
      x
       = 
       
       
      sec
      (
      (
      x
      +
      27
      )
      )
    • , then
    • x
    • =
  • (i)
    7
  • (ii)
    6
  • (iii)
    4
  • (iv)
    9
  • (v)
    8
Question 22
22.
    • If
    • V
    • ,
    • W
    •  
    • and
    •  
    • X
    • are the interior angles of a triangle, then
    •  
    • sin
      (
      V + W

      2
      )
    •  
    • =
  • (i)
    sin
    (
    X

    2
    )
  • (ii)
    sin
    (
    V

    2
    )
  • (iii)
    sin
    X
  • (iv)
    cos
    (
    X

    2
    )
  • (v)
    cos
    (
    V

    2
    )
Question 23
23.
Which of the following are true?
a)
sin
52°
 = 
cos
52°
b)
sin
31°
 = 
cos
59°
c)
sec
22°
 = 
cosec
68°
d)
sin
30°
 = 
cos
60°
e)
cos
20°
 = 
sin
20°
f)
sin
23°
 = 
cos
67°
g)
tan
28°
 = 
cot
62°
  • (i)
    {a,e,d}
  • (ii)
    {a,f,g}
  • (iii)
    {e,c}
  • (iv)
    {a,b}
  • (v)
    {b,c,d,f,g}
Question 24
24.
Which of the following are true?
a)
    • cosec
      90°
    • is not defined
b)
    • sec
    • is not defined
c)
    • cosec
    • is not defined
d)
    • tan
    • is not defined
e)
    • sec
      90°
    • is not defined
f)
    • cot
    • is not defined
g)
    • tan
      90°
    • is not defined
h)
    • cot
      90°
    • is not defined
  • (i)
    {d,h,f}
  • (ii)
    {b,e}
  • (iii)
    {c,e,f,g}
  • (iv)
    {a,c}
  • (v)
    {a,g,c}
Question 25
25.
Which of the following are true?
a)
 
 
sec
θ
 = 
 
 
1

 
 
sin
θ
b)
 
 
cosec
θ
 = 
 
 
1

 
 
sin
θ
c)
 
 
cot
θ
 = 
 
 
1

 
 
sec
θ
d)
 
 
sec
θ
 = 
 
 
1

 
 
cos
θ
e)
 
 
cos
θ
 = 
 
 
1

 
 
cosec
θ
f)
 
 
tan
θ
 = 
 
 
1

 
 
cot
θ
  • (i)
    {e,a,f}
  • (ii)
    {c,d}
  • (iii)
    {b,d,f}
  • (iv)
    {c,b,d}
  • (v)
    {a,b}
Question 26
26.
Which of the following are true?
a)
sin
 = 
1
b)
cos
90°
 = 
1
c)
cos
45°
 = 
1
d)
cos
 = 
1
e)
sin
45°
 = 
1
f)
tan
90°
 = 
1
g)
tan
 = 
1
h)
sin
90°
 = 
1
  • (i)
    {d,h}
  • (ii)
    {b,h}
  • (iii)
    {f,h,d}
  • (iv)
    {a,d}
  • (v)
    {c,e,d}
Question 27
27.
Which of the following are true?
a)
tan
90°
 = 
0
b)
cos
45°
 = 
0
c)
cos
90°
 = 
0
d)
sin
45°
 = 
0
e)
sin
 = 
0
f)
tan
 = 
0
g)
sin
90°
 = 
0
h)
cos
 = 
0
  • (i)
    {c,e,f}
  • (ii)
    {d,g,f}
  • (iii)
    {b,e}
  • (iv)
    {h,c,e}
  • (v)
    {a,c}
Question 28
28.
Which of the following are true?
a)
    • cot
      (
      90
        +  
      θ
      )
    • =
    •    
      tan
      θ
b)
    • cosec
      (
      90
        +  
      θ
      )
    • =
    •    
      cosec
      θ
c)
    • sec
      (
      90
        +  
      θ
      )
    • =
    •    
      cosec
      θ
d)
    • cosec
      (
      90
        +  
      θ
      )
    • =
    • sec
      θ
e)
    • cot
      (
      90
        +  
      θ
      )
    • =
    •    
      cot
      θ
f)
    • sec
      (
      90
        +  
      θ
      )
    • =
    •    
      sec
      θ
  • (i)
    {e,c}
  • (ii)
    {f,b,d}
  • (iii)
    {b,a}
  • (iv)
    {a,c,d}
  • (v)
    {e,a,c}
Question 29
29.
Which of the following are true?
a)
    • tan
      (
      90
        +  
      θ
      )
    • =
    •    
      cot
      θ
b)
    • cos
      (
      90
        +  
      θ
      )
    • =
    •    
      cos
      θ
c)
    • sin
      (
      90
        +  
      θ
      )
    • =
    •    
      sin
      θ
d)
    • cos
      (
      90
        +  
      θ
      )
    • =
    •    
      sin
      θ
e)
    • tan
      (
      90
        +  
      θ
      )
    • =
    •    
      tan
      θ
f)
    • sin
      (
      90
        +  
      θ
      )
    • =
    • cos
      θ
  • (i)
    {e,b,f}
  • (ii)
    {c,d}
  • (iii)
    {b,a}
  • (iv)
    {a,d,f}
  • (v)
    {c,a,d}
Question 30
30.
Which of the following are true?
a)
    • sin
      (
         
      θ
      )
    • =
    • sin
      θ
b)
    • cos
      (
         
      θ
      )
    • =
    • cos
      θ
c)
    • tan
      (
         
      θ
      )
    • =
    • tan
      θ
d)
    • tan
      (
         
      θ
      )
    • =
    • tan
      θ
e)
    • sin
      (
         
      θ
      )
    • =
    • sin
      θ
f)
    • cos
      (
         
      θ
      )
    • =
    • cos
      θ
  • (i)
    {a,d}
  • (ii)
    {c,a,f}
  • (iii)
    {b,d,e}
  • (iv)
    {b,e}
  • (v)
    {d,e,f}
Question 31
31.
Which of the following are true?
a)
    • sec
      (
         
      θ
      )
    • =
    • sec
      θ
b)
    • cosec
      (
         
      θ
      )
    • =
    • cosec
      θ
c)
    • sec
      (
         
      θ
      )
    • =
    • sec
      θ
d)
    • cot
      (
         
      θ
      )
    • =
    • cot
      θ
e)
    • cot
      (
         
      θ
      )
    • =
    • cot
      θ
f)
    • cosec
      (
         
      θ
      )
    • =
    • cosec
      θ
  • (i)
    {d,c}
  • (ii)
    {d,b,c}
  • (iii)
    {f,a,e}
  • (iv)
    {b,c,e}
  • (v)
    {a,b}
Question 32
32.
    • If
    •  
    • w
    • =
    • cos
      θ
        +  
      sin
      θ
    • ,
    • x
    • =
    • cos
      θ
      sin
      θ
    • then
  • (i)
    (
    w
    2
     
    +
    x
    2
     
    )
     = 
    1
  • (ii)
    (
    w
    2
     
    x
    2
     
    )
     = 
    1
  • (iii)
    w
    2
     
     = 
    (
    2
    x
    +
    1
    )
  • (iv)
    w
    2
     
     = 
    (
    2
    x
    +
    1
    )
  • (v)
    (
    w
    2
     
    +
    x
    2
     
    )
     = 
    0
Question 33
33.
    • If
    •  
    • q
    • =
    • cos
      θ
        +  
      sin
      θ
    • ,
    • r
    • =
    • cos
      θ
         
      sin
      θ
    • then
  • (i)
    (
    q
    2
     
    r
    2
     
    )
     = 
    1
  • (ii)
    (
    q
    2
     
    +
    r
    2
     
    )
     = 
    2
  • (iii)
    (
    q
    2
     
    r
    2
     
    )
     = 
    2
  • (iv)
    (
    q
    2
     
    +
    r
    2
     
    )
     = 
    1
  • (v)
    (
    q
    2
     
    +
    r
    2
     
    )
     = 
    0
Question 34
34.
a)
    •  
       
      y
      2
       

       
       
      z
      2
       
    • =
    • tan
      2
       
      θ
b)
    • 2
      y
      z
    • =
    • e
      2
       
    • sin
      2
      θ
c)
    • (
      y
      +
      z
      )
      2
    • =
    • e
      2
       
d)
    • (
      y
      2
       
      +
      z
      2
       
      )
       = 
      e
      2
       
e)
    • (
      y
      2
       
      z
      2
       
      )
       = 
      e
      2
       
  • (i)
    {c,e,d}
  • (ii)
    {c,a,b}
  • (iii)
    {e,b}
  • (iv)
    {c,a}
  • (v)
    {a,b,d}
Question 35
35.
    • If
    •  
    • a
    • =
    • p
    • cos
      θ
    • +
    • q
    • sin
      θ
    •  
    • and
    •  
    • b
    • =
    • p
    • sin
      θ
    • q
    • cos
      θ
    • , then
  • (i)
    a
    b
     = 
    p
    q
  • (ii)
    (
    p
    2
     
    +
    a
    2
     
    )
     = 
    (
    q
    2
     
    +
    b
    2
     
    )
  • (iii)
    (
    a
    2
     
    +
    b
    2
     
    )
     = 
    (
    p
    2
     
    +
    q
    2
     
    )
  • (iv)
    (
    a
    2
     
    b
    2
     
    )
     = 
    (
    p
    2
     
    q
    2
     
    )
    Assignment Key

  •  1) (iii)
  •  2) (iii)
  •  3) (i)
  •  4) (ii)
  •  5) (iv)
  •  6) (v)
  •  7) (iii)
  •  8) (ii)
  •  9) (ii)
  •  10) (iv)
  •  11) (i)
  •  12) (iv)
  •  13) (iii)
  •  14) (v)
  •  15) (iii)
  •  16) (i)
  •  17) (iv)
  •  18) (ii)
  •  19) (v)
  •  20) (ii)
  •  21) (i)
  •  22) (iv)
  •  23) (v)
  •  24) (iii)
  •  25) (iii)
  •  26) (i)
  •  27) (i)
  •  28) (iv)
  •  29) (iv)
  •  30) (v)
  •  31) (iv)
  •  32) (iii)
  •  33) (ii)
  •  34) (v)
  •  35) (iii)