EduSahara™ Assignment
Name : Trigonometry Miscellaneous
Chapter : Introduction to Trigonometry
Grade : CBSE Grade X
License : Non Commercial Use
Question
1
1.
Which of the following are true?
a)
The value of
tan
C
is always less than 1
b)
The value of
sin
C
is always less than 1
c)
cos
C
is the abbrieviation for
cosec
C
d)
If
sin
C
= 0 , then
cos
C
= 1 or
cos
C
= -1
e)
The value of
cot
C
is always less than 1
(i)
{c,d,b}
(ii)
{c,d}
(iii)
{b,d}
(iv)
{a,b}
(v)
{e,a,b}
Question
2
2.
For angle values from 0° to 90°, which of the following are true?
a)
The cotangent value of the angle increases
b)
The sine value of the angle increases
c)
The tangent value of the angle increases
d)
The cosine value of the angle increases
e)
The product of the sine and cosine values remains a constant
f)
The sum of the squares of the sine and cosine values remains a constant
(i)
{d,b,c}
(ii)
{a,b}
(iii)
{e,a,f}
(iv)
{b,c,f}
(v)
{d,c}
Question
3
3.
Which of the following are true?
a)
The cosecant of an angle is the reciprocal of the secant of the angle
b)
cos
(
E
+
F
)
=
cos
E
+
cos
F
c)
tan
E
= tan
✕
E
d)
The cotangent of an angle is the reciprocal of the tangent of the angle.
e)
sin
(
E
+
F
)
=
sin
E
+
sin
F
f)
The cosine value of an angle is the reciprocal of the sine of the angle.
(i)
{c,e,d}
(ii)
{d}
(iii)
{f,d}
(iv)
{b,d}
(v)
{a,d}
Question
4
4.
Which of the following are true?
a)
cos
(
D
+
E
)
=
cos
D
+
cos
E
b)
The value of
sin
θ
increases as
θ
increases from
0°
to
90°
c)
The value of
cos
θ
increases as
θ
increases from
0°
to
90°
d)
sin
θ
=
cos
θ
for all
θ
e)
sin
(
D
+
E
)
=
sin
D
+
sin
E
f)
tan
(
D
+
E
)
=
tan
D
+
tan
E
g)
tan
θ
=
cot
θ
for no value of
θ
(i)
{d,e,b}
(ii)
{f,b}
(iii)
{a,b}
(iv)
{b}
(v)
{c,b}
Question
5
5.
Which of the following are true?
a)
sin
2
A
=
2
sin
A
cos
A
b)
sin
2
A
=
2
sin
2
A
cos
2
A
c)
cos
2
A
=
cos
2
A
−
sin
2
A
d)
cos
2
A
=
cos
2
A
+
sin
2
A
e)
tan
2
A
=
2
tan
A
1
+
tan
2
A
f)
tan
2
A
=
2
tan
A
1
−
tan
2
A
(i)
{d,a,c}
(ii)
{d,c}
(iii)
{a,c,f}
(iv)
{b,a}
(v)
{e,b,f}
Question
6
6.
Which of the following are true?
a)
cos
140°
=
cos
2
70°
+
sin
2
70°
b)
sin
140°
=
2
sin
2
70°
cos
2
70°
c)
tan
140°
=
2
tan
70°
1
+
tan
2
70°
d)
cos
140°
=
cos
2
70°
−
sin
2
70°
e)
tan
140°
=
2
tan
70°
1
−
tan
2
70°
f)
sin
140°
=
2
sin
70°
cos
70°
(i)
{c,a,f}
(ii)
{b,e}
(iii)
{b,d,e}
(iv)
{a,d}
(v)
{d,e,f}
Question
7
7.
Which of the following are true?
a)
1
+
sin
θ
cos
θ
+
cos
θ
1
+
sin
θ
=
2
sec
θ
b)
cos
θ
1
−
sin
θ
+
cos
θ
1
+
sin
θ
=
2
c)
cos
θ
cosec
θ
+
1
+
cos
θ
cosec
θ
−
1
=
2
tan
θ
d)
(
sec
θ
−
tan
θ
)
2
=
1
+
sin
θ
1
−
sin
θ
e)
(
sec
θ
−
tan
θ
)
2
=
1
−
sin
θ
1
+
sin
θ
(i)
{d,c}
(ii)
{a,c,e}
(iii)
{b,d,e}
(iv)
{b,a}
(v)
{b,a,c}
Question
8
8.
Which of the following are true?
a)
(
sin
θ
−
cos
θ
)
2
=
1
+
sin
2
θ
b)
(
sin
θ
+
cos
θ
)
2
+
(
sin
θ
−
cos
θ
)
2
=
2
c)
cos
3
θ
+
sin
3
θ
=
(
sin
θ
+
cos
θ
)
(
1
−
sin
θ
cos
θ
)
d)
(
sin
θ
+
cos
θ
)
2
=
1
+
sin
2
θ
e)
cos
θ
1
+
sin
θ
=
1
−
sin
θ
cos
θ
f)
cos
3
θ
−
sin
3
θ
=
(
sin
θ
+
cos
θ
)
(
1
−
sin
θ
cos
θ
)
g)
sec
θ
1
+
cosec
θ
=
1
−
cosec
θ
sec
θ
(i)
{f,e,b}
(ii)
{f,c}
(iii)
{a,b}
(iv)
{b,c,d,e}
(v)
{g,a,d}
Question
9
9.
If
Q
,
R
and
S
are the interior angles of a triangle, then
sin
(
Q + R
2
)
=
(i)
cos
(
S
2
)
(ii)
sin
(
S
2
)
(iii)
cos
(
Q
2
)
(iv)
sin
S
(v)
sin
(
Q
2
)
Question
10
10.
Which of the following are true?
a)
sin
55°
=
cos
35°
b)
sin
44°
=
cos
44°
c)
sin
53°
=
cos
37°
d)
sin
39°
=
cos
51°
e)
tan
38°
=
cot
52°
f)
sec
33°
=
cosec
57°
g)
cos
48°
=
sin
48°
(i)
{g,c}
(ii)
{b,e,f}
(iii)
{a,c,d,e,f}
(iv)
{b,g,d}
(v)
{b,a}
Question
11
11.
Which of the following are true?
a)
cosec
90°
is not defined
b)
sec
90°
is not defined
c)
cot
0°
is not defined
d)
cot
90°
is not defined
e)
sec
0°
is not defined
f)
tan
90°
is not defined
g)
cosec
0°
is not defined
h)
tan
0°
is not defined
(i)
{d,c}
(ii)
{e,h,f}
(iii)
{b,c,f,g}
(iv)
{a,b}
(v)
{a,g,b}
Question
12
12.
Which of the following are true?
a)
sec
θ
=
1
cos
θ
b)
cosec
θ
=
1
sin
θ
c)
cos
θ
=
1
cosec
θ
d)
sec
θ
=
1
sin
θ
e)
tan
θ
=
1
cot
θ
f)
cot
θ
=
1
sec
θ
(i)
{f,c,e}
(ii)
{a,b,e}
(iii)
{d,a,b}
(iv)
{d,b}
(v)
{c,a}
Question
13
13.
Which of the following are true?
a)
cos
45°
=
1
b)
sin
90°
=
1
c)
sin
45°
=
1
d)
sin
0°
=
1
e)
tan
90°
=
1
f)
cos
90°
=
1
g)
cos
0°
=
1
h)
tan
0°
=
1
(i)
{f,g,b}
(ii)
{c,g}
(iii)
{a,b}
(iv)
{d,e,b}
(v)
{b,g}
Question
14
14.
Which of the following are true?
a)
tan
90°
=
0
b)
cos
90°
=
0
c)
cos
45°
=
0
d)
cos
0°
=
0
e)
sin
0°
=
0
f)
sin
45°
=
0
g)
sin
90°
=
0
h)
tan
0°
=
0
(i)
{c,e}
(ii)
{g,b,e}
(iii)
{b,e,h}
(iv)
{d,f,h}
(v)
{a,b}
Question
15
15.
If
w
=
cos
θ
+
sin
θ
,
x
=
cos
θ
sin
θ
then
(i)
w
2
=
(
2
x
+
1
)
(ii)
(
w
2
+
x
2
)
=
1
(iii)
w
2
=
(
−
2
x
+
1
)
(iv)
(
w
2
−
x
2
)
=
1
(v)
(
w
2
+
x
2
)
=
0
Question
16
16.
If
v
=
cos
θ
+
sin
θ
,
w
=
cos
θ
−
sin
θ
then
(i)
(
v
2
−
w
2
)
=
1
(ii)
(
v
2
+
w
2
)
=
2
(iii)
(
v
2
+
w
2
)
=
0
(iv)
(
v
2
+
w
2
)
=
1
(v)
(
v
2
−
w
2
)
=
2
Question
17
17.
a)
(
y
+
z
)
2
=
g
2
b)
2
y
z
=
g
2
sin
2
θ
c)
(
y
2
−
z
2
)
=
g
2
d)
(
y
2
+
z
2
)
=
g
2
e)
y
2
z
2
=
tan
2
θ
(i)
{a,c,e}
(ii)
{c,d}
(iii)
{b,d,e}
(iv)
{a,b}
(v)
{a,b,d}
Question
18
18.
If
c
=
v
cos
θ
+
w
sin
θ
and
d
=
v
sin
θ
−
w
cos
θ
, then
(i)
(
v
2
+
c
2
)
=
(
w
2
+
d
2
)
(ii)
(
c
2
−
d
2
)
=
(
v
2
−
w
2
)
(iii)
(
c
2
+
d
2
)
=
(
v
2
+
w
2
)
(iv)
c
d
=
v
w
Assignment Key
1) (iii)
2) (iv)
3) (ii)
4) (iv)
5) (iii)
6) (v)
7) (ii)
8) (iv)
9) (i)
10) (iii)
11) (iii)
12) (ii)
13) (v)
14) (iii)
15) (i)
16) (ii)
17) (iii)
18) (iii)
