EduSahara™ Worksheet
Name : Chapter Based Worksheet
Chapter : Trigonometry
Grade : SSC Grade X
License : Non Commercial Use
Question
1
1.
Express
sin
39°
in terms of
cos
39°
(i)
1
cos
39°
(ii)
√
1
−
cos
2
39°
cos
39°
(iii)
√
1
−
cos
2
39°
(iv)
cos
39°
√
1
−
cos
2
39°
(v)
1
√
1
−
cos
2
39°
Question
2
2.
Given
cos
P
=
3
5
,
find
sin
P
(i)
5
3
(ii)
4
3
(iii)
5
4
(iv)
4
5
(v)
3
4
Question
3
3.
In the given figure, △IJK is a right angle triangle with ∠K = 90° and JK = 17 cm. Q is the mid-point of IK. Find the length of the altitude from K to IJ.
(i)
17
√
3
cm
(ii)
17
2
√
2
cm
(iii)
17
2
cm
(iv)
17
4
√
12
cm
(v)
17
cm
Question
4
4.
Express
cosec
θ
in terms of
tan
θ
(i)
√
1
+
tan
2
θ
tan
θ
(ii)
tan
θ
√
1
+
tan
2
θ
(iii)
1
√
1
+
tan
2
θ
(iv)
√
1
+
tan
2
θ
(v)
1
tan
θ
Question
5
5.
In
△IJK
, right angled at
J
,
if
IJ = 15 cm
and
JK = 8 cm
,
find
tan
K
(i)
15
8
(ii)
17
8
(iii)
5
2
(iv)
3
2
(v)
13
8
Question
6
6.
Express
cos
35°
in terms of
cot
35°
(i)
1
cot
35°
(ii)
1
√
1
+
cot
2
35°
(iii)
cot
35°
√
1
+
cot
2
35°
(iv)
√
1
+
cot
2
35°
cot
35°
(v)
√
1
+
cot
2
35°
Question
7
7.
Express
cos
θ
in terms of
tan
θ
(i)
tan
θ
√
1
+
tan
2
θ
(ii)
√
1
+
tan
2
θ
tan
θ
(iii)
1
√
1
+
tan
2
θ
(iv)
√
1
+
tan
2
θ
(v)
1
tan
θ
Question
8
8.
tan
69°
−
cot
21°
=
(i)
0
(ii)
2
sin
69°
(iii)
2
sin
21°
(iv)
1
(v)
-1
Question
9
9.
Which of the following are true?
a)
sin
47°
=
cos
43°
b)
sec
52°
=
cosec
38°
c)
sin
33°
=
cos
33°
d)
sin
39°
=
cos
51°
e)
cos
37°
=
sin
37°
f)
tan
23°
=
cot
67°
g)
sin
36°
=
cos
54°
(i)
{a,b,d,f,g}
(ii)
{c,a}
(iii)
{c,f,g}
(iv)
{c,e,d}
(v)
{e,b}
Question
10
10.
Express
cos
64°
in terms of
cosec
64°
(i)
1
cosec
64°
(ii)
√
cosec
2
64°
−
1
cosec
64°
(iii)
cosec
64°
√
cosec
2
64°
−
1
(iv)
√
cosec
2
64°
−
1
(v)
1
√
cosec
2
64°
−
1
Question
11
11.
Express
sec
θ
in terms of
cosec
θ
(i)
√
cosec
2
θ
−
1
cosec
θ
(ii)
cosec
θ
√
cosec
2
θ
−
1
(iii)
√
cosec
2
θ
−
1
(iv)
1
√
cosec
2
θ
−
1
(v)
1
cosec
θ
Question
12
12.
In the given figure,
cosec
K
=
(i)
7
4
(ii)
5
6
(iii)
5
2
(iv)
3
4
(v)
5
4
Question
13
13.
Find the value of
3
sec
2
θ
−
3
tan
2
θ
(i)
0
(ii)
1
(iii)
3
(iv)
5
Question
14
14.
Express
cosec
θ
in terms of
cot
θ
(i)
√
1
+
cot
2
θ
(ii)
1
√
1
+
cot
2
θ
(iii)
cot
θ
√
1
+
cot
2
θ
(iv)
1
cot
θ
(v)
√
1
+
cot
2
θ
cot
θ
Question
15
15.
Given
cot
E
=
√
15
,
find
tan
E
(i)
4
15
√
15
(ii)
4
(iii)
1
4
(iv)
1
15
√
15
(v)
1
4
√
15
Question
16
16.
In the given figure, △BDC is right angled at C. If BC = 22 cm and ∠D = 60°, find BE
(i)
33
cm
(ii)
33
2
√
2
cm
(iii)
11
√
18
cm
(iv)
11
√
3
cm
(v)
11
cm
Question
17
17.
Given
tan
B
=
8
15
,
find
sec
B
(i)
8
17
(ii)
17
8
(iii)
15
17
(iv)
15
8
(v)
17
15
Question
18
18.
Given
cosec
C
=
17
8
,
find
sin
C
(i)
8
15
(ii)
15
17
(iii)
8
17
(iv)
15
8
(v)
17
15
Question
19
19.
Given
tan
J
=
5
39
√
39
,
find
cot
J
(i)
1
5
√
39
(ii)
5
8
(iii)
8
39
√
39
(iv)
8
5
(v)
1
8
√
39
Question
20
20.
sin
60°
tan
60°
cos
0°
−
sec
60°
cot
45°
cosec
30°
=
(i)
(
−
5
2
)
(ii)
(
−
7
2
)
(iii)
(
−
3
2
)
(iv)
(
−
5
4
)
(v)
(
−
5
)
Question
21
21.
Express
tan
68°
in terms of
cos
68°
(i)
√
1
−
cos
2
68°
(ii)
cos
68°
√
1
−
cos
2
68°
(iii)
√
1
−
cos
2
68°
cos
68°
(iv)
1
cos
68°
(v)
1
√
1
−
cos
2
68°
Question
22
22.
In the given figure, △CED is right angled at D. If CD = 12 cm and ∠E = 45°, find DE
(i)
9
cm
(ii)
11
cm
(iii)
15
cm
(iv)
13
cm
(v)
12
cm
Question
23
23.
Express
sin
θ
in terms of
cos
θ
(i)
cos
θ
√
1
−
cos
2
θ
(ii)
1
√
1
−
cos
2
θ
(iii)
√
1
−
cos
2
θ
cos
θ
(iv)
√
1
−
cos
2
θ
(v)
1
cos
θ
Question
24
24.
Express
sec
θ
in terms of
cot
θ
(i)
1
√
1
+
cot
2
θ
(ii)
1
cot
θ
(iii)
cot
θ
√
1
+
cot
2
θ
(iv)
√
1
+
cot
2
θ
(v)
√
1
+
cot
2
θ
cot
θ
Question
25
25.
In the given figure,
cosec
C
=
(i)
CD
ED
(ii)
FD
FE
(iii)
CE
DE
(iv)
ED
CD
(v)
DC
DE
Assignment Key
1) (iii)
2) (iv)
3) (ii)
4) (i)
5) (i)
6) (iii)
7) (iii)
8) (i)
9) (i)
10) (ii)
11) (ii)
12) (v)
13) (iii)
14) (i)
15) (iv)
16) (iv)
17) (v)
18) (iii)
19) (i)
20) (i)
21) (iii)
22) (v)
23) (iv)
24) (v)
25) (iii)
