EduSahara™ Worksheet
Name : Chapter Based Worksheet
Chapter : Trigonometrical Identities
Grade : ICSE Grade X
License : Non Commercial Use
Question
1
1.
Express
tan
θ
in terms of
cot
θ
(i)
cot
θ
√
1
+
cot
2
θ
(ii)
√
1
+
cot
2
θ
(iii)
√
1
+
cot
2
θ
cot
θ
(iv)
1
cot
θ
(v)
1
√
1
+
cot
2
θ
Question
2
2.
Which of the following are true?
a)
sin
30°
=
cos
60°
b)
sec
55°
=
cosec
35°
c)
cos
53°
=
sin
53°
d)
tan
25°
=
cot
65°
e)
sin
28°
=
cos
28°
f)
sin
39°
=
cos
51°
g)
sin
41°
=
cos
49°
(i)
{e,b}
(ii)
{c,e,d}
(iii)
{c,f,g}
(iv)
{c,a}
(v)
{a,b,d,f,g}
Question
3
3.
In the given figure, △HIJ is right angled at I. If IJ = 8 cm and ∠J = 30°, find HI and HJ
(i)
8
3
cm
&
18
cm
(ii)
8
3
4
√
3
cm
&
16
cm
(iii)
8
3
4
√
3
cm
&
18
cm
(iv)
8
3
4
√
3
cm
&
16
3
√
3
cm
(v)
8
3
√
3
cm
&
16
3
√
3
cm
Question
4
4.
From the given figure,
find
cosec
(
90
−
F
)
(i)
DF
EF
(ii)
DE
DF
(iii)
EF
DE
(iv)
DE
EF
(v)
DF
DE
Question
5
5.
If
q
=
cos
θ
+
sin
θ
,
r
=
cos
θ
sin
θ
then
(i)
q
2
=
(
2
r
+
1
)
(ii)
(
q
2
+
r
2
)
=
0
(iii)
q
2
=
(
−
2
r
+
1
)
(iv)
(
q
2
+
r
2
)
=
1
(v)
(
q
2
−
r
2
)
=
1
Question
6
6.
In the given figure,
sec
M
=
(i)
1
(ii)
7
3
(iii)
5
(iv)
5
3
Question
7
7.
Express
tan
33°
in terms of
sin
33°
(i)
√
1
−
sin
2
33°
sin
33°
(ii)
1
sin
33°
(iii)
sin
33°
√
1
−
sin
2
33°
(iv)
√
1
−
sin
2
33°
(v)
1
√
1
−
sin
2
33°
Question
8
8.
Which of the following are true?
a)
cot
(
90
+
θ
)
=
−
cot
θ
b)
cosec
(
90
+
θ
)
=
sec
θ
c)
cot
(
90
+
θ
)
=
−
tan
θ
d)
sec
(
90
+
θ
)
=
−
cosec
θ
e)
cosec
(
90
+
θ
)
=
−
cosec
θ
f)
sec
(
90
+
θ
)
=
−
sec
θ
(i)
{e,c}
(ii)
{f,a,d}
(iii)
{a,b}
(iv)
{b,c,d}
(v)
{e,b,c}
Question
9
9.
The value of
cot
302°
in terms of an angle between
0°
and
90°
is
(i)
−
cot
32°
(ii)
cot
32°
(iii)
−
tan
32°
(iv)
tan
32°
Question
10
10.
In the given figure, △DFE is right angled at E. If DE = 15 cm and ∠F = 45°, find EF
(i)
14
cm
(ii)
12
cm
(iii)
17
cm
(iv)
16
cm
(v)
15
cm
Question
11
11.
Express
cot
θ
in terms of
cos
θ
(i)
cos
θ
√
1
−
cos
2
θ
(ii)
√
1
−
cos
2
θ
cos
θ
(iii)
1
cos
θ
(iv)
√
1
−
cos
2
θ
(v)
1
√
1
−
cos
2
θ
Question
12
12.
sec
7°
−
cosec
83°
=
(i)
0
(ii)
1
(iii)
2
sin
7°
(iv)
2
sin
83°
(v)
-1
Question
13
13.
Given that
12
sec
θ
=
13
, find
cos
θ
(i)
13
5
(ii)
5
13
(iii)
12
5
(iv)
5
12
(v)
12
13
Question
14
14.
tan
64°
cot
75°
−
cot
26°
tan
15°
=
(i)
2
sin
64°
(ii)
0
(iii)
1
(iv)
2
sin
75°
(v)
-1
Question
15
15.
Express
cot
θ
in terms of
sin
θ
(i)
1
sin
θ
(ii)
sin
θ
√
1
−
sin
2
θ
(iii)
√
1
−
sin
2
θ
(iv)
√
1
−
sin
2
θ
sin
θ
(v)
1
√
1
−
sin
2
θ
Question
16
16.
In
△FGH
, right angled at
G
,
if
FG = 15 cm
and
GH = 8 cm
,
find
cosec
H
(i)
17
15
(ii)
1
(iii)
17
13
(iv)
19
15
Question
17
17.
Given
cot
H
=
4
3
,
find
cos
H
(i)
3
4
(ii)
5
4
(iii)
3
5
(iv)
4
5
(v)
5
3
Question
18
18.
cot
45°
=
(i)
3
(ii)
1
(iii)
(
−
2
)
(iv)
0
(v)
2
Question
19
19.
Given
cosec
J
=
5
4
,
find
sin
J
(i)
3
4
(ii)
4
3
(iii)
4
5
(iv)
5
3
(v)
3
5
Question
20
20.
Which of the following are true?
a)
cos
(
180
+
θ
)
=
sin
θ
b)
tan
(
180
+
θ
)
=
cot
θ
c)
tan
(
180
+
θ
)
=
tan
θ
d)
cos
(
180
+
θ
)
=
−
cos
θ
e)
sin
(
180
+
θ
)
=
cos
θ
f)
sin
(
180
+
θ
)
=
−
sin
θ
(i)
{a,c}
(ii)
{e,a,f}
(iii)
{b,c,d}
(iv)
{c,d,f}
(v)
{b,d}
Question
21
21.
The value of
cosec
340°
in terms of an angle between
0°
and
90°
is
(i)
−
sec
70°
(ii)
cosec
70°
(iii)
−
cosec
70°
(iv)
sec
70°
Question
22
22.
In the given figure,
sin
C
=
(i)
35
37
(ii)
35
39
(iii)
33
37
(iv)
1
Question
23
23.
Given
sec
B
=
2
3
√
3
,
find
sin
B
(i)
1
2
√
3
(ii)
√
3
(iii)
1
3
√
3
(iv)
2
(v)
1
2
Question
24
24.
Given that
12
tan
θ
=
5
, find
cosec
θ
(i)
13
12
(ii)
5
13
(iii)
13
5
(iv)
12
5
(v)
12
13
Question
25
25.
Which of the following are true?
a)
cos
(
360
+
θ
)
=
cos
θ
b)
cos
(
360
+
θ
)
=
sin
θ
c)
tan
(
360
+
θ
)
=
tan
θ
d)
sin
(
360
+
θ
)
=
sin
θ
e)
tan
(
360
+
θ
)
=
cot
θ
f)
sin
(
360
+
θ
)
=
cos
θ
(i)
{e,a,c}
(ii)
{e,c}
(iii)
{f,b,d}
(iv)
{b,a}
(v)
{a,c,d}
Assignment Key
1) (iv)
2) (v)
3) (v)
4) (i)
5) (i)
6) (iv)
7) (iii)
8) (iv)
9) (iii)
10) (v)
11) (i)
12) (i)
13) (v)
14) (ii)
15) (iv)
16) (i)
17) (iv)
18) (ii)
19) (iii)
20) (iv)
21) (i)
22) (i)
23) (v)
24) (iii)
25) (v)
