EduSahara™ Worksheet
Name : Chapter Based Worksheet
Chapter : Introduction to Trigonometry
Grade : CBSE Grade X
License : Non Commercial Use
Question
1
1.
Which of the following are true?
a)
sec
2
θ
+
tan
2
θ
=
1
,
0 ≤ θ ≤ 90°
b)
cosec
2
θ
+
cot
2
θ
=
1
,
0 ≤ θ ≤ 90°
c)
sin
2
θ
+
cos
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)
{a,c}
(ii)
{f,a,e}
(iii)
{b,d}
(iv)
{c,d,e}
(v)
{b,c,d}
Question
2
2.
If
tan
θ
+
cot
θ
=
3
, find
tan
2
θ
+
cot
2
θ
(i)
7
(ii)
9
(iii)
6
(iv)
4
(v)
8
Question
3
3.
Given
cos
E
=
3
5
,
find
sec
E
(i)
4
3
(ii)
5
4
(iii)
3
4
(iv)
5
3
(v)
4
5
Question
4
4.
Given that
17
cos
θ
=
15
, find
sec
θ
(i)
17
8
(ii)
17
15
(iii)
8
17
(iv)
8
15
(v)
15
8
Question
5
5.
The value of
sec
283°
in terms of an angle between
0°
and
90°
is
(i)
−
sec
13°
(ii)
cosec
13°
(iii)
sec
13°
(iv)
−
cosec
13°
Question
6
6.
Which of the following are true?
a)
cot
0°
is not defined
b)
tan
90°
is not defined
c)
sec
90°
is not defined
d)
cosec
0°
is not defined
e)
cot
90°
is not defined
f)
cosec
90°
is not defined
g)
tan
0°
is not defined
h)
sec
0°
is not defined
(i)
{e,d,a}
(ii)
{a,b,c,d}
(iii)
{f,b}
(iv)
{g,h,c}
(v)
{e,a}
Question
7
7.
cos
19°
+
sin
57°
=
(i)
cos
19°
+
cos
57°
(ii)
sin
71°
+
sin
33°
(iii)
sin
71°
+
cos
33°
(iv)
sin
19°
+
cos
57°
Question
8
8.
The value of
tan
250°
in terms of an angle between
0°
and
90°
is
(i)
tan
70°
(ii)
−
tan
70°
(iii)
cot
70°
(iv)
−
cot
70°
Question
9
9.
Given that
5
sin
θ
=
4
, find
cos
θ
(i)
5
4
(ii)
4
3
(iii)
5
3
(iv)
3
5
(v)
3
4
Question
10
10.
Given
cos
C
=
1
2
√
3
,
find
tan
C
(i)
2
(ii)
1
3
√
3
(iii)
√
3
(iv)
1
2
(v)
2
3
√
3
Question
11
11.
Which of the following are true?
a)
sec
(
270
−
θ
)
=
−
sec
θ
b)
cot
(
270
−
θ
)
=
tan
θ
c)
cot
(
270
−
θ
)
=
cot
θ
d)
cosec
(
270
−
θ
)
=
−
cosec
θ
e)
sec
(
270
−
θ
)
=
−
cosec
θ
f)
cosec
(
270
−
θ
)
=
−
sec
θ
(i)
{d,a,f}
(ii)
{c,e}
(iii)
{c,b,e}
(iv)
{a,b}
(v)
{b,e,f}
Question
12
12.
Given
cosec
N
=
3
2
,
find
sec
N
(i)
3
5
√
5
(ii)
2
3
(iii)
1
2
√
5
(iv)
2
5
√
5
(v)
1
3
√
5
Question
13
13.
From the given figure,
find
tan
(
90
−
D
)
(i)
BC
BD
(ii)
CD
BC
(iii)
CD
BD
(iv)
BD
BC
(v)
BD
CD
Question
14
14.
If
w
=
cos
θ
+
sin
θ
,
x
=
cos
θ
sin
θ
then
(i)
(
w
2
−
x
2
)
=
1
(ii)
(
w
2
+
x
2
)
=
0
(iii)
w
2
=
(
2
x
+
1
)
(iv)
w
2
=
(
−
2
x
+
1
)
(v)
(
w
2
+
x
2
)
=
1
Question
15
15.
In the given figure, △ACB is right angled at B. If AB = 26 cm and ∠C = 60°, find BC
(i)
26
3
√
3
cm
(ii)
26
cm
(iii)
26
3
√
18
cm
(iv)
13
√
2
cm
(v)
26
3
cm
Question
16
16.
Express
cot
θ
in terms of
cos
θ
(i)
1
√
1
−
cos
2
θ
(ii)
1
cos
θ
(iii)
√
1
−
cos
2
θ
(iv)
√
1
−
cos
2
θ
cos
θ
(v)
cos
θ
√
1
−
cos
2
θ
Question
17
17.
From the given figure,
find
cos
(
90
−
C
)
(i)
DE
CD
(ii)
DE
CE
(iii)
CE
CD
(iv)
CD
CE
(v)
CD
DE
Question
18
18.
Express
cos
θ
in terms of
sec
θ
(i)
sec
θ
√
sec
2
θ
−
1
(ii)
1
sec
θ
(iii)
1
√
sec
2
θ
−
1
(iv)
√
sec
2
θ
−
1
sec
θ
(v)
√
sec
2
θ
−
1
Question
19
19.
In the given figure,
cot
N
=
(i)
4
(ii)
12
7
(iii)
2
(iv)
14
5
(v)
12
5
Question
20
20.
Given that
5
sin
θ
=
3
, find
cosec
θ
(i)
4
5
(ii)
5
3
(iii)
3
4
(iv)
4
3
(v)
5
4
Question
21
21.
sec
G
=
(i)
1
tan
G
(ii)
1
cot
G
(iii)
1
cos
G
(iv)
1
cosec
G
(v)
1
sin
G
Question
22
22.
cot
55°
tan
83°
−
tan
35°
cot
7°
=
(i)
0
(ii)
1
(iii)
-1
(iv)
2
sin
55°
(v)
2
sin
83°
Question
23
23.
Which of the following are true?
a)
sec
(
270
+
θ
)
=
cosec
θ
b)
cosec
(
270
+
θ
)
=
−
sec
θ
c)
cot
(
270
+
θ
)
=
−
tan
θ
d)
sec
(
270
+
θ
)
=
sec
θ
e)
cosec
(
270
+
θ
)
=
−
cosec
θ
f)
cot
(
270
+
θ
)
=
−
cot
θ
(i)
{e,a,b}
(ii)
{d,a}
(iii)
{e,b}
(iv)
{f,d,c}
(v)
{a,b,c}
Question
24
24.
Which of the following are true?
a)
sin
(
−
θ
)
=
sin
θ
b)
sin
(
−
θ
)
=
−
sin
θ
c)
cos
(
−
θ
)
=
−
cos
θ
d)
tan
(
−
θ
)
=
−
tan
θ
e)
cos
(
−
θ
)
=
cos
θ
f)
tan
(
−
θ
)
=
tan
θ
(i)
{b,d,e}
(ii)
{a,b}
(iii)
{f,a,e}
(iv)
{c,d}
(v)
{c,b,d}
Question
25
25.
sin
5°
cos
85°
=
(i)
tan
5°
(ii)
-1
(iii)
0
(iv)
tan
85°
(v)
1
Assignment Key
1) (iv)
2) (i)
3) (iv)
4) (ii)
5) (ii)
6) (ii)
7) (iii)
8) (i)
9) (iv)
10) (ii)
11) (v)
12) (i)
13) (ii)
14) (iii)
15) (i)
16) (v)
17) (ii)
18) (ii)
19) (v)
20) (ii)
21) (iii)
22) (i)
23) (v)
24) (i)
25) (v)
