EduSahara™ Worksheet
Name : Chapter Based Worksheet
Chapter : Trigonometrical Identities
Grade : ICSE Grade X
License : Non Commercial Use
Question
1
1.
In
△MNO
, right angled at
N
,
if
MN = 35 cm
and
NO = 12 cm
,
find
tan
M
(i)
12
37
(ii)
12
35
(iii)
2
7
(iv)
4
11
(v)
2
5
Question
2
2.
Given
sin
B
=
1
7
,
find
cosec
B
(i)
4
√
3
(ii)
1
12
√
3
(iii)
7
12
√
3
(iv)
4
7
√
3
(v)
7
Question
3
3.
tan
G
=
(i)
1
cos
G
(ii)
1
cot
G
(iii)
1
sin
G
(iv)
1
cosec
G
(v)
1
sec
G
Question
4
4.
Which of the following are true?
a)
sin
(
180
−
θ
)
=
cos
θ
b)
tan
(
180
−
θ
)
=
−
cot
θ
c)
tan
(
180
−
θ
)
=
−
tan
θ
d)
sin
(
180
−
θ
)
=
sin
θ
e)
cos
(
180
−
θ
)
=
−
sin
θ
f)
cos
(
180
−
θ
)
=
−
cos
θ
(i)
{b,c,d}
(ii)
{a,c}
(iii)
{c,d,f}
(iv)
{e,a,f}
(v)
{b,d}
Question
5
5.
If
cot
5
x
=
tan
(
(
x
+
18
)
)
, then
x
=
(i)
15
(ii)
13
(iii)
9
(iv)
11
(v)
12
Question
6
6.
Given that
5
sin
θ
=
4
, find
sec
θ
(i)
5
4
(ii)
5
3
(iii)
3
4
(iv)
4
3
(v)
3
5
Question
7
7.
The value of
cosec
242°
in terms of an angle between
0°
and
90°
is
(i)
sec
62°
(ii)
−
sec
62°
(iii)
cosec
62°
(iv)
−
cosec
62°
Question
8
8.
In the given figure,
tan
C
=
(i)
CD
EC
(ii)
ED
CE
(iii)
DE
CD
(iv)
DE
EC
(v)
FE
ED
Question
9
9.
sin
(
A
−
B
)
=
(i)
cos
A
cos
B
−
sin
A
sin
B
(ii)
sin
A
cos
B
+
cos
A
sin
B
(iii)
sin
A
cos
B
−
cos
A
sin
B
(iv)
cos
A
cos
B
+
sin
A
sin
B
Question
10
10.
Given that
5
sin
θ
=
4
, find
tan
θ
(i)
5
3
(ii)
3
4
(iii)
3
5
(iv)
5
4
(v)
4
3
Question
11
11.
Given
tan
P
=
1
4
√
2
,
find
cos
P
(i)
2
3
√
2
(ii)
3
(iii)
1
3
(iv)
2
√
2
(v)
3
4
√
2
Question
12
12.
Which of the following are true?
a)
sin
(
180
+
θ
)
=
cos
θ
b)
cos
(
180
+
θ
)
=
−
cos
θ
c)
tan
(
180
+
θ
)
=
tan
θ
d)
tan
(
180
+
θ
)
=
cot
θ
e)
cos
(
180
+
θ
)
=
sin
θ
f)
sin
(
180
+
θ
)
=
−
sin
θ
(i)
{d,b,c}
(ii)
{e,a,f}
(iii)
{b,c,f}
(iv)
{a,b}
(v)
{d,c}
Question
13
13.
sin
K
=
(i)
1
cosec
K
(ii)
1
tan
K
(iii)
1
cot
K
(iv)
1
cos
K
(v)
1
sec
K
Question
14
14.
Given that
12
sec
θ
=
13
, find
cot
θ
(i)
12
5
(ii)
12
13
(iii)
5
12
(iv)
13
5
(v)
5
13
Question
15
15.
A chord of 13 cm subtends an angle of 90° at the centre. Calculate its shortest distance from the centre
(i)
8.5 cm
(ii)
5.5 cm
(iii)
4.5 cm
(iv)
6.5 cm
(v)
7.5 cm
Question
16
16.
Which of the following are true?
a)
sec
θ
=
1
cos
θ
b)
cosec
θ
=
1
sin
θ
c)
sec
θ
=
1
sin
θ
d)
cot
θ
=
1
sec
θ
e)
tan
θ
=
1
cot
θ
f)
cos
θ
=
1
cosec
θ
(i)
{d,a,b}
(ii)
{d,b}
(iii)
{c,a}
(iv)
{f,c,e}
(v)
{a,b,e}
Question
17
17.
Given
cosec
B
=
13
5
,
find
cos
B
(i)
5
13
(ii)
12
5
(iii)
13
12
(iv)
12
13
(v)
5
12
Question
18
18.
Given that
13
cos
θ
=
12
, find
tan
θ
(i)
13
12
(ii)
5
12
(iii)
5
13
(iv)
12
5
(v)
13
5
Question
19
19.
Find angle
θ
such that
cos
θ
=
0.6997
From Table of Natural Cosines
x°
0'
6'
12'
18'
24'
30'
36'
42'
48'
54'
1'
2'
3'
4'
5'
45
0.7071
0.7059
0.7046
0.7034
0.7022
0.7009
0.6997
0.6984
0.6972
0.6959
2
4
6
8
10
(i)
45
°
31
'
(ii)
45
°
46
'
(iii)
45
°
26
'
(iv)
45
°
36
'
(v)
45
°
41
'
Question
20
20.
Express
cos
55°
in terms of
tan
55°
(i)
√
1
+
tan
2
55°
(ii)
1
√
1
+
tan
2
55°
(iii)
tan
55°
√
1
+
tan
2
55°
(iv)
√
1
+
tan
2
55°
tan
55°
(v)
1
tan
55°
Question
21
21.
cosec
60°
=
(i)
2
4
√
1
3
(ii)
2
√
1
3
(iii)
2
(iv)
2
√
-1
3
(v)
2
3
Question
22
22.
Given that
17
cos
θ
=
15
, find
cot
θ
(i)
17
8
(ii)
8
17
(iii)
17
15
(iv)
15
8
(v)
8
15
Question
23
23.
Given
cot
B
=
4
3
,
find
sin
B
(i)
5
3
(ii)
4
5
(iii)
3
4
(iv)
3
5
(v)
5
4
Question
24
24.
1
+
tan
2
θ
1
+
cot
2
θ
=
(i)
sec
2
θ
(ii)
cot
2
θ
(iii)
cosec
2
θ
(iv)
tan
2
θ
(v)
1
Question
25
25.
Which of the following are true?
a)
cos
(
−
θ
)
=
cos
θ
b)
tan
(
−
θ
)
=
−
tan
θ
c)
tan
(
−
θ
)
=
tan
θ
d)
sin
(
−
θ
)
=
sin
θ
e)
sin
(
−
θ
)
=
−
sin
θ
f)
cos
(
−
θ
)
=
−
cos
θ
(i)
{a,b,e}
(ii)
{d,b}
(iii)
{d,a,b}
(iv)
{c,a}
(v)
{f,c,e}
Assignment Key
1) (ii)
2) (v)
3) (ii)
4) (iii)
5) (v)
6) (ii)
7) (iv)
8) (iii)
9) (iii)
10) (v)
11) (i)
12) (iii)
13) (i)
14) (i)
15) (iv)
16) (v)
17) (iv)
18) (ii)
19) (iv)
20) (ii)
21) (ii)
22) (iv)
23) (iv)
24) (iv)
25) (i)
