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
B
is always less than 1
b)
cos
B
is the abbrieviation for
cosec
B
c)
The value of
sin
B
is always less than 1
d)
The value of
cot
B
is always less than 1
e)
If
sin
B
= 0 , then
cos
B
= 1 or
cos
B
= -1
(i)
{b,e,c}
(ii)
{c,e}
(iii)
{d,a,c}
(iv)
{a,c}
(v)
{b,e}
Question
2
2.
For angle values from 0° to 90°, which of the following are true?
a)
The sine value of the angle increases
b)
The tangent value of the angle increases
c)
The cosine value of the angle increases
d)
The sum of the squares of the sine and cosine values remains a constant
e)
The cotangent value of the angle increases
f)
The product of the sine and cosine values remains a constant
(i)
{e,b}
(ii)
{c,a}
(iii)
{f,c,d}
(iv)
{a,b,d}
(v)
{e,a,b}
Question
3
3.
Which of the following are true?
a)
The cosine value of an angle is the reciprocal of the sine of the angle.
b)
sin
(
F
+
G
)
=
sin
F
+
sin
G
c)
The cosecant of an angle is the reciprocal of the secant of the angle
d)
cos
(
F
+
G
)
=
cos
F
+
cos
G
e)
The cotangent of an angle is the reciprocal of the tangent of the angle.
f)
tan
F
= tan
✕
F
(i)
{e}
(ii)
{f,e}
(iii)
{c,d,e}
(iv)
{b,e}
(v)
{a,e}
Question
4
4.
Which of the following are true?
a)
sin
θ
=
cos
θ
for all
θ
b)
The value of
cos
θ
increases as
θ
increases from
0°
to
90°
c)
sin
(
E
+
F
)
=
sin
E
+
sin
F
d)
tan
(
E
+
F
)
=
tan
E
+
tan
F
e)
The value of
sin
θ
increases as
θ
increases from
0°
to
90°
f)
tan
θ
=
cot
θ
for no value of
θ
g)
cos
(
E
+
F
)
=
cos
E
+
cos
F
(i)
{f,e}
(ii)
{a,e}
(iii)
{b,e}
(iv)
{e}
(v)
{c,d,e}
Question
5
5.
Which of the following are true?
a)
tan
2
A
=
2
tan
A
1
+
tan
2
A
b)
sin
2
A
=
2
sin
A
cos
A
c)
sin
2
A
=
2
sin
2
A
cos
2
A
d)
cos
2
A
=
cos
2
A
+
sin
2
A
e)
tan
2
A
=
2
tan
A
1
−
tan
2
A
f)
cos
2
A
=
cos
2
A
−
sin
2
A
(i)
{b,e,f}
(ii)
{d,a,f}
(iii)
{a,b}
(iv)
{c,e}
(v)
{c,b,e}
Question
6
6.
Which of the following are true?
a)
tan
108°
=
2
tan
54°
1
+
tan
2
54°
b)
sin
108°
=
2
sin
54°
cos
54°
c)
cos
108°
=
cos
2
54°
+
sin
2
54°
d)
sin
108°
=
2
sin
2
54°
cos
2
54°
e)
cos
108°
=
cos
2
54°
−
sin
2
54°
f)
tan
108°
=
2
tan
54°
1
−
tan
2
54°
(i)
{a,b}
(ii)
{d,a,f}
(iii)
{c,b,e}
(iv)
{c,e}
(v)
{b,e,f}
Question
7
7.
Which of the following are true?
a)
cos
θ
1
−
sin
θ
+
cos
θ
1
+
sin
θ
=
2
b)
cos
θ
cosec
θ
+
1
+
cos
θ
cosec
θ
−
1
=
2
tan
θ
c)
1
+
sin
θ
cos
θ
+
cos
θ
1
+
sin
θ
=
2
sec
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,b,c}
(iii)
{a,b}
(iv)
{b,c,e}
(v)
{a,d,e}
Question
8
8.
Which of the following are true?
a)
cos
θ
1
+
sin
θ
=
1
−
sin
θ
cos
θ
b)
sec
θ
1
+
cosec
θ
=
1
−
cosec
θ
sec
θ
c)
cos
3
θ
−
sin
3
θ
=
(
sin
θ
+
cos
θ
)
(
1
−
sin
θ
cos
θ
)
d)
cos
3
θ
+
sin
3
θ
=
(
sin
θ
+
cos
θ
)
(
1
−
sin
θ
cos
θ
)
e)
(
sin
θ
+
cos
θ
)
2
=
1
+
sin
2
θ
f)
(
sin
θ
+
cos
θ
)
2
+
(
sin
θ
−
cos
θ
)
2
=
2
g)
(
sin
θ
−
cos
θ
)
2
=
1
+
sin
2
θ
(i)
{b,a}
(ii)
{a,d,e,f}
(iii)
{c,d}
(iv)
{g,b,e}
(v)
{c,f,a}
Question
9
9.
If
U
,
V
and
W
are the interior angles of a triangle, then
sin
(
U + V
2
)
=
(i)
sin
(
U
2
)
(ii)
sin
(
W
2
)
(iii)
cos
(
W
2
)
(iv)
cos
(
U
2
)
(v)
sin
W
Question
10
10.
Which of the following are true?
a)
sin
50°
=
cos
50°
b)
sec
21°
=
cosec
69°
c)
sin
54°
=
cos
36°
d)
sin
35°
=
cos
55°
e)
sin
27°
=
cos
63°
f)
tan
40°
=
cot
50°
g)
cos
48°
=
sin
48°
(i)
{a,e,f}
(ii)
{g,c}
(iii)
{a,b}
(iv)
{b,c,d,e,f}
(v)
{a,g,d}
Question
11
11.
Which of the following are true?
a)
tan
0°
is not defined
b)
cot
90°
is not defined
c)
sec
0°
is not defined
d)
tan
90°
is not defined
e)
cot
0°
is not defined
f)
cosec
90°
is not defined
g)
sec
90°
is not defined
h)
cosec
0°
is not defined
(i)
{d,e,g,h}
(ii)
{a,d}
(iii)
{b,e}
(iv)
{c,f,g}
(v)
{a,h,d}
Question
12
12.
Which of the following are true?
a)
cot
θ
=
1
sec
θ
b)
cosec
θ
=
1
sin
θ
c)
cos
θ
=
1
cosec
θ
d)
tan
θ
=
1
cot
θ
e)
sec
θ
=
1
sin
θ
f)
sec
θ
=
1
cos
θ
(i)
{e,a,f}
(ii)
{c,d}
(iii)
{b,d,f}
(iv)
{c,b,d}
(v)
{a,b}
Question
13
13.
Which of the following are true?
a)
cos
45°
=
1
b)
tan
0°
=
1
c)
cos
90°
=
1
d)
sin
0°
=
1
e)
sin
45°
=
1
f)
sin
90°
=
1
g)
tan
90°
=
1
h)
cos
0°
=
1
(i)
{e,h,f}
(ii)
{f,h}
(iii)
{b,h}
(iv)
{a,f}
(v)
{c,d,f}
Question
14
14.
Which of the following are true?
a)
cos
90°
=
0
b)
sin
0°
=
0
c)
sin
45°
=
0
d)
cos
45°
=
0
e)
cos
0°
=
0
f)
tan
90°
=
0
g)
tan
0°
=
0
h)
sin
90°
=
0
(i)
{e,f,g}
(ii)
{a,b,g}
(iii)
{d,b}
(iv)
{h,a,b}
(v)
{c,a}
Question
15
15.
If
v
=
cos
θ
+
sin
θ
,
w
=
cos
θ
sin
θ
then
(i)
(
v
2
+
w
2
)
=
0
(ii)
(
v
2
−
w
2
)
=
1
(iii)
v
2
=
(
−
2
w
+
1
)
(iv)
(
v
2
+
w
2
)
=
1
(v)
v
2
=
(
2
w
+
1
)
Question
16
16.
If
v
=
cos
θ
+
sin
θ
,
w
=
cos
θ
−
sin
θ
then
(i)
(
v
2
−
w
2
)
=
2
(ii)
(
v
2
+
w
2
)
=
0
(iii)
(
v
2
+
w
2
)
=
2
(iv)
(
v
2
+
w
2
)
=
1
(v)
(
v
2
−
w
2
)
=
1
Question
17
17.
a)
2
p
q
=
b
2
sin
2
θ
b)
p
2
q
2
=
tan
2
θ
c)
(
p
2
+
q
2
)
=
b
2
d)
(
p
2
−
q
2
)
=
b
2
e)
(
p
+
q
)
2
=
b
2
(i)
{a,b,c}
(ii)
{d,a,b}
(iii)
{d,a}
(iv)
{d,e,c}
(v)
{e,b}
Question
18
18.
If
f
=
x
cos
θ
+
y
sin
θ
and
g
=
x
sin
θ
−
y
cos
θ
, then
(i)
(
f
2
+
g
2
)
=
(
x
2
+
y
2
)
(ii)
(
x
2
+
f
2
)
=
(
y
2
+
g
2
)
(iii)
f
g
=
x
y
(iv)
(
f
2
−
g
2
)
=
(
x
2
−
y
2
)
Assignment Key
1) (ii)
2) (iv)
3) (i)
4) (iv)
5) (i)
6) (v)
7) (iv)
8) (ii)
9) (iii)
10) (iv)
11) (i)
12) (iii)
13) (ii)
14) (ii)
15) (v)
16) (iii)
17) (i)
18) (i)
