EduSahara™ Worksheet
Name : Chapter Based Worksheet
Chapter : Trigonometry
Grade : SSC Grade X
License : Non Commercial Use
Question
1
1.
From the given figure,
find
cos
(
90
−
H
)
(i)
HI
HJ
(ii)
IJ
HJ
(iii)
HJ
HI
(iv)
IJ
HI
(v)
HI
IJ
Question
2
2.
Express
cosec
55°
in terms of
sin
55°
(i)
1
√
1
−
sin
2
55°
(ii)
√
1
−
sin
2
55°
sin
55°
(iii)
sin
55°
√
1
−
sin
2
55°
(iv)
√
1
−
sin
2
55°
(v)
1
sin
55°
Question
3
3.
In the given figure, △EGF is right angled at F. If EF = 22 cm and ∠G = 60°, find FG
(i)
22
3
√
18
cm
(ii)
11
√
2
cm
(iii)
22
3
cm
(iv)
22
3
√
3
cm
(v)
22
cm
Question
4
4.
Which of the following are true?
a)
sin
2
θ
+
cos
2
θ
=
1
,
0 ≤ θ ≤ 90°
b)
sec
2
θ
+
tan
2
θ
=
1
,
0 ≤ θ ≤ 90°
c)
cosec
2
θ
−
cot
2
θ
=
1
,
0 ≤ θ ≤ 90°
d)
cosec
2
θ
+
cot
2
θ
=
1
,
0 ≤ θ ≤ 90°
e)
sec
2
θ
−
tan
2
θ
=
1
,
0 ≤ θ ≤ 90°
f)
sin
2
θ
−
cos
2
θ
=
1
,
0 ≤ θ ≤ 90°
(i)
{d,a,c}
(ii)
{f,b,e}
(iii)
{a,c,e}
(iv)
{b,a}
(v)
{d,c}
Question
5
5.
Express
cot
38°
in terms of
sin
38°
(i)
1
sin
38°
(ii)
√
1
−
sin
2
38°
sin
38°
(iii)
√
1
−
sin
2
38°
(iv)
sin
38°
√
1
−
sin
2
38°
(v)
1
√
1
−
sin
2
38°
Question
6
6.
Given
sec
M
=
5
12
√
6
,
find
sin
M
(i)
1
5
(ii)
2
5
√
6
(iii)
1
12
√
6
(iv)
2
√
6
(v)
5
Question
7
7.
Given
sin
H
=
4
5
,
find
sec
H
(i)
3
4
(ii)
3
5
(iii)
4
3
(iv)
5
4
(v)
5
3
Question
8
8.
tan
60°
=
(i)
3
(ii)
4
√
3
(iii)
√
3
(iv)
√
5
(v)
√
1
3
Question
9
9.
In the given figure,
cosec
G
=
(i)
EG
EF
(ii)
HF
GF
(iii)
FE
GE
(iv)
GF
EF
(v)
EF
GF
Question
10
10.
Given
cos
H
=
1
4
√
7
,
find
cot
H
(i)
3
7
√
7
(ii)
4
3
(iii)
4
7
√
7
(iv)
3
4
(v)
1
3
√
7
Question
11
11.
Given
tan
A
=
4
65
√
65
,
find
cosec
A
(i)
9
4
(ii)
9
65
√
65
(iii)
1
9
√
65
(iv)
4
9
(v)
1
4
√
65
Question
12
12.
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
13
13.
In the given figure, if
CE
+
DE
=
32 cm
,
and
CD = 8 cm
,
find
cos
C
(i)
6
17
(ii)
8
19
(iii)
8
15
(iv)
8
17
(v)
10
17
Question
14
14.
In the given figure, △BCD is a right angle triangle with ∠D = 90° and CD = 15 cm. R is the mid-point of BD. Find the length of the altitude from D to BC.
(i)
15
2
√
18
cm
(ii)
15
2
√
3
cm
(iii)
45
4
√
2
cm
(iv)
45
2
cm
(v)
15
2
cm
Question
15
15.
cot
33°
tan
57°
=
(i)
1
(ii)
tan
33°
(iii)
tan
57°
(iv)
-1
(v)
0
Question
16
16.
sin
90°
cos
60°
+
cos
90°
sin
60°
=
(i)
1
2
(ii)
1
4
(iii)
1
(iv)
(
−
1
2
)
(v)
3
2
Question
17
17.
cot
49°
tan
29°
tan
41°
cot
61°
=
(i)
1
(ii)
tan
29°
(iii)
-1
(iv)
tan
49°
(v)
0
Question
18
18.
cosec
32°
+
sec
47°
=
(i)
cosec
32°
+
cosec
47°
(ii)
sec
58°
+
cosec
43°
(iii)
sec
32°
+
cosec
47°
(iv)
sec
58°
+
sec
43°
Question
19
19.
Given
cos
J
=
4
5
,
find
sin
J
(i)
5
4
(ii)
5
3
(iii)
3
5
(iv)
3
4
(v)
4
3
Question
20
20.
cos
79°
+
sin
64°
=
(i)
sin
11°
+
sin
26°
(ii)
sin
79°
+
cos
64°
(iii)
sin
11°
+
cos
26°
(iv)
cos
79°
+
cos
64°
Question
21
21.
Given that
15
sec
θ
=
17
, find
cot
θ
(i)
8
15
(ii)
17
8
(iii)
15
8
(iv)
8
17
(v)
15
17
Question
22
22.
Express
cosec
θ
in terms of
sin
θ
(i)
1
√
1
−
sin
2
θ
(ii)
√
1
−
sin
2
θ
(iii)
√
1
−
sin
2
θ
sin
θ
(iv)
sin
θ
√
1
−
sin
2
θ
(v)
1
sin
θ
Question
23
23.
Given
cot
J
=
4
3
,
find
sec
J
(i)
3
4
(ii)
5
4
(iii)
5
3
(iv)
4
5
(v)
3
5
Question
24
24.
If
cos
4
x
=
sin
(
(
x
+
25
)
)
, then
x
=
(i)
14
(ii)
16
(iii)
13
(iv)
12
(v)
10
Question
25
25.
Find the value of
(
1
+
sin
θ
)
(
cos
θ
)
+
(
cos
θ
)
(
1
+
sin
θ
)
(i)
2
sin
θ
(ii)
2
sec
θ
(iii)
2
cos
θ
(iv)
2
cosec
θ
Assignment Key
1) (ii)
2) (v)
3) (iv)
4) (iii)
5) (ii)
6) (i)
7) (v)
8) (iii)
9) (i)
10) (v)
11) (i)
12) (ii)
13) (iv)
14) (ii)
15) (i)
16) (i)
17) (i)
18) (ii)
19) (iii)
20) (iii)
21) (iii)
22) (v)
23) (ii)
24) (iii)
25) (ii)
