EduSahara™ Worksheet
Name : Chapter Based Worksheet
Chapter : Introduction to Trigonometry
Grade : CBSE Grade X
License : Non Commercial Use
Question
1
1.
sec
21°
cosec
12°
−
cosec
69°
sec
78°
=
(i)
2
sin
12°
(ii)
2
sin
21°
(iii)
-1
(iv)
0
(v)
1
Question
2
2.
Given
cos
J
=
3
8
√
7
,
find
tan
J
(i)
3
√
7
(ii)
8
(iii)
1
8
(iv)
8
21
√
7
(v)
1
21
√
7
Question
3
3.
sin
(
A
+
B
)
=
(i)
cos
A
cos
B
−
sin
A
sin
B
(ii)
sin
A
cos
B
−
cos
A
sin
B
(iii)
cos
A
cos
B
+
sin
A
sin
B
(iv)
sin
A
cos
B
+
cos
A
sin
B
Question
4
4.
Which of the following are true?
a)
sin
(
360
+
θ
)
=
sin
θ
b)
tan
(
360
+
θ
)
=
tan
θ
c)
cos
(
360
+
θ
)
=
sin
θ
d)
tan
(
360
+
θ
)
=
cot
θ
e)
cos
(
360
+
θ
)
=
cos
θ
f)
sin
(
360
+
θ
)
=
cos
θ
(i)
{d,b}
(ii)
{c,a}
(iii)
{f,c,e}
(iv)
{d,a,b}
(v)
{a,b,e}
Question
5
5.
Given
cosec
H
=
13
5
,
find
cos
H
(i)
12
13
(ii)
13
12
(iii)
5
13
(iv)
5
12
(v)
12
5
Question
6
6.
Which of the following are true?
a)
cot
(
180
−
θ
)
=
−
tan
θ
b)
sec
(
180
−
θ
)
=
−
sec
θ
c)
cosec
(
180
−
θ
)
=
sec
θ
d)
cot
(
180
−
θ
)
=
−
cot
θ
e)
cosec
(
180
−
θ
)
=
cosec
θ
f)
sec
(
180
−
θ
)
=
−
cosec
θ
(i)
{b,d,e}
(ii)
{c,b,d}
(iii)
{c,d}
(iv)
{f,a,e}
(v)
{a,b}
Question
7
7.
Given
cosec
K
=
13
5
,
find
tan
K
(i)
13
12
(ii)
5
12
(iii)
12
5
(iv)
12
13
(v)
5
13
Question
8
8.
Express
cot
θ
in terms of
sec
θ
(i)
sec
θ
√
sec
2
θ
−
1
(ii)
√
sec
2
θ
−
1
sec
θ
(iii)
1
sec
θ
(iv)
√
sec
2
θ
−
1
(v)
1
√
sec
2
θ
−
1
Question
9
9.
Express
sec
θ
in terms of
cosec
θ
(i)
cosec
θ
√
cosec
2
θ
−
1
(ii)
1
√
cosec
2
θ
−
1
(iii)
√
cosec
2
θ
−
1
(iv)
1
cosec
θ
(v)
√
cosec
2
θ
−
1
cosec
θ
Question
10
10.
Given
tan
E
=
1
3
√
3
,
find
sin
E
(i)
1
2
(ii)
1
2
√
3
(iii)
2
3
√
3
(iv)
2
(v)
√
3
Question
11
11.
In the given figure,
sec
H
=
(i)
GF
GH
(ii)
IG
IH
(iii)
FG
FH
(iv)
FH
GH
(v)
HG
HF
Question
12
12.
Express
sec
θ
in terms of
tan
θ
(i)
1
√
1
+
tan
2
θ
(ii)
√
1
+
tan
2
θ
tan
θ
(iii)
tan
θ
√
1
+
tan
2
θ
(iv)
1
tan
θ
(v)
√
1
+
tan
2
θ
Question
13
13.
Given
cosec
D
=
2
,
find
tan
D
(i)
2
3
√
3
(ii)
1
2
√
3
(iii)
1
3
√
3
(iv)
1
2
(v)
√
3
Question
14
14.
Express
tan
48°
in terms of
sin
48°
(i)
1
sin
48°
(ii)
sin
48°
√
1
−
sin
2
48°
(iii)
1
√
1
−
sin
2
48°
(iv)
√
1
−
sin
2
48°
(v)
√
1
−
sin
2
48°
sin
48°
Question
15
15.
Given
cot
A
=
4
3
,
find
sin
A
(i)
5
3
(ii)
5
4
(iii)
3
5
(iv)
3
4
(v)
4
5
Question
16
16.
Express
cosec
θ
in terms of
sec
θ
(i)
1
√
sec
2
θ
−
1
(ii)
sec
θ
√
sec
2
θ
−
1
(iii)
1
sec
θ
(iv)
√
sec
2
θ
−
1
sec
θ
(v)
√
sec
2
θ
−
1
Question
17
17.
Which of the following are true?
a)
cos
60°
=
cos
2
30°
−
sin
2
30°
b)
sin
60°
=
2
sin
30°
cos
30°
c)
tan
60°
=
2
tan
30°
1
+
tan
2
30°
d)
cos
60°
=
cos
2
30°
+
sin
2
30°
e)
tan
60°
=
2
tan
30°
1
−
tan
2
30°
f)
sin
60°
=
2
sin
2
30°
cos
2
30°
(i)
{d,b}
(ii)
{f,c,e}
(iii)
{d,a,b}
(iv)
{c,a}
(v)
{a,b,e}
Question
18
18.
The value of
cosec
133°
in terms of an angle between
0°
and
90°
is
(i)
sec
43°
(ii)
cosec
43°
(iii)
−
cosec
43°
(iv)
−
sec
43°
Question
19
19.
Which of the following are true?
a)
cosec
(
270
−
θ
)
=
−
cosec
θ
b)
cot
(
270
−
θ
)
=
tan
θ
c)
sec
(
270
−
θ
)
=
−
sec
θ
d)
sec
(
270
−
θ
)
=
−
cosec
θ
e)
cot
(
270
−
θ
)
=
cot
θ
f)
cosec
(
270
−
θ
)
=
−
sec
θ
(i)
{c,b,d}
(ii)
{c,d}
(iii)
{b,d,f}
(iv)
{a,b}
(v)
{e,a,f}
Question
20
20.
Which of the following are true?
a)
1
+
sin
θ
cos
θ
+
cos
θ
1
+
sin
θ
=
2
sec
θ
b)
cos
θ
cosec
θ
+
1
+
cos
θ
cosec
θ
−
1
=
2
tan
θ
c)
(
sec
θ
−
tan
θ
)
2
=
1
+
sin
θ
1
−
sin
θ
d)
(
sec
θ
−
tan
θ
)
2
=
1
−
sin
θ
1
+
sin
θ
e)
cos
θ
1
−
sin
θ
+
cos
θ
1
+
sin
θ
=
2
(i)
{c,a}
(ii)
{c,e,d}
(iii)
{e,b}
(iv)
{a,b,d}
(v)
{c,a,b}
Question
21
21.
In the given figure,
sec
I
=
(i)
7
3
(ii)
1
(iii)
5
3
(iv)
5
Question
22
22.
Given
cot
C
=
√
15
,
find
sec
C
(i)
1
4
√
15
(ii)
1
15
√
15
(iii)
4
15
√
15
(iv)
1
4
(v)
4
Question
23
23.
Given
tan
D
=
1
3
√
3
,
find
cosec
D
(i)
1
2
√
3
(ii)
2
3
√
3
(iii)
1
2
(iv)
√
3
(v)
2
Question
24
24.
In the given figure, if
CE
+
DE
=
50 cm
,
and
CD = 10 cm
,
find
tan
C
(i)
12
5
(ii)
2
(iii)
14
5
(iv)
4
(v)
12
7
Question
25
25.
Express
cosec
θ
in terms of
cot
θ
(i)
1
cot
θ
(ii)
1
√
1
+
cot
2
θ
(iii)
√
1
+
cot
2
θ
cot
θ
(iv)
√
1
+
cot
2
θ
(v)
cot
θ
√
1
+
cot
2
θ
Assignment Key
1) (iv)
2) (v)
3) (iv)
4) (v)
5) (i)
6) (i)
7) (ii)
8) (v)
9) (i)
10) (i)
11) (iv)
12) (v)
13) (iii)
14) (ii)
15) (iii)
16) (ii)
17) (v)
18) (i)
19) (iii)
20) (iv)
21) (iii)
22) (iii)
23) (v)
24) (i)
25) (iv)
