EduSahara™ Worksheet
Name : Chapter Based Worksheet
Chapter : Trigonometrical Identities
Grade : ICSE Grade X
License : Non Commercial Use
Question
1
1.
cot
60°
−
tan
30°
=
(i)
2
sin
60°
(ii)
1
(iii)
0
(iv)
2
sin
30°
(v)
-1
Question
2
2.
In the given figure, △ACB is right angled at B. If AB = 13 cm and ∠C = 45°, find AC
(i)
26
cm
(ii)
13
2
√
12
cm
(iii)
13
√
2
cm
(iv)
13
cm
(v)
26
√
3
cm
Question
3
3.
From the given figure,
find
cosec
(
90
−
B
)
(i)
BD
CD
(ii)
BD
BC
(iii)
BC
CD
(iv)
CD
BD
(v)
CD
BC
Question
4
4.
Find the value of
cos
48
°
10
'
From Table of Natural Cosines
x°
0'
6'
12'
18'
24'
30'
36'
42'
48'
54'
1'
2'
3'
4'
5'
48
0.6691
0.6678
0.6665
0.6652
0.6639
0.6626
0.6613
0.6600
0.6587
0.6574
2
4
7
9
11
(i)
0.6673
(ii)
0.6672
(iii)
0.6669
(iv)
0.6665
(v)
0.6666
Question
5
5.
The value of
tan
335°
in terms of an angle between
0°
and
90°
is
(i)
cot
65°
(ii)
−
tan
65°
(iii)
tan
65°
(iv)
−
cot
65°
Question
6
6.
Given that
4
sec
θ
=
5
, find
sin
θ
(i)
5
3
(ii)
3
4
(iii)
4
3
(iv)
4
5
(v)
3
5
Question
7
7.
cot
60°
=
(i)
4
√
1
3
(ii)
1
(iii)
√
-1
3
(iv)
√
1
3
(v)
1
3
Question
8
8.
Express
sec
θ
in terms of
sin
θ
(i)
√
1
−
sin
2
θ
(ii)
sin
θ
√
1
−
sin
2
θ
(iii)
√
1
−
sin
2
θ
sin
θ
(iv)
1
sin
θ
(v)
1
√
1
−
sin
2
θ
Question
9
9.
1
−
tan
2
θ
1
+
tan
2
θ
=
(i)
cot
2
θ
(ii)
sin
2
θ
(iii)
cos
2
θ
(iv)
tan
2
θ
Question
10
10.
Given
sin
G
=
1
2
,
find
cosec
G
(i)
√
3
(ii)
2
(iii)
1
3
√
3
(iv)
2
3
√
3
(v)
1
2
√
3
Question
11
11.
Express
cot
θ
in terms of
tan
θ
(i)
√
1
+
tan
2
θ
(ii)
√
1
+
tan
2
θ
tan
θ
(iii)
tan
θ
√
1
+
tan
2
θ
(iv)
1
tan
θ
(v)
1
√
1
+
tan
2
θ
Question
12
12.
In
△FGH
, right angled at
G
,
if
FG = 35 cm
and
GH = 12 cm
,
find
cot
H
(i)
2
7
(ii)
2
5
(iii)
4
11
(iv)
12
37
(v)
12
35
Question
13
13.
sec
11°
cosec
79°
=
(i)
1
(ii)
tan
79°
(iii)
tan
11°
(iv)
-1
(v)
0
Question
14
14.
In
△HIJ
, right angled at
I
,
if
tan
H
=
2
5
,
find
cos
H
cos
J
−
sin
H
sin
J
(i)
5
29
√
29
(ii)
1
2
√
29
(iii)
2
29
√
29
(iv)
1
5
√
29
(v)
0
Question
15
15.
Express
sin
θ
in terms of
tan
θ
(i)
1
tan
θ
(ii)
tan
θ
√
1
+
tan
2
θ
(iii)
1
√
1
+
tan
2
θ
(iv)
√
1
+
tan
2
θ
(v)
√
1
+
tan
2
θ
tan
θ
Question
16
16.
Express
sec
θ
in terms of
cot
θ
(i)
1
cot
θ
(ii)
cot
θ
√
1
+
cot
2
θ
(iii)
√
1
+
cot
2
θ
(iv)
√
1
+
cot
2
θ
cot
θ
(v)
1
√
1
+
cot
2
θ
Question
17
17.
Which of the following are true?
a)
cos
F
is the abbrieviation for
cosec
F
b)
The value of
sin
F
is always less than 1
c)
If
sin
F
= 0 , then
cos
F
= 1 or
cos
F
= -1
d)
The value of
cot
F
is always less than 1
e)
The value of
tan
F
is always less than 1
(i)
{a,b}
(ii)
{d,c,b}
(iii)
{e,a,b}
(iv)
{b,c}
(v)
{d,c}
Question
18
18.
If
sin
5
x
=
cos
(
(
x
+
60
)
)
, then
x
=
(i)
5
(ii)
7
(iii)
3
(iv)
6
(v)
4
Question
19
19.
Find the area of an isosceles triangle with base 6 cm and vertical angle 65°
(i)
16.1265 cm
(ii)
14.1265 cm
(iii)
13.1265 cm
(iv)
15.1265 cm
Question
20
20.
From the given figure,
find
sec
(
90
−
L
)
(i)
JL
KL
(ii)
KL
JK
(iii)
JL
JK
(iv)
KL
JL
(v)
JK
KL
Question
21
21.
In the given figure, if
HJ
+
IJ
=
32 cm
,
and
HI = 8 cm
,
find
tan
H
(i)
5
2
(ii)
15
8
(iii)
17
8
(iv)
13
8
(v)
3
2
Question
22
22.
Which of the following are true?
a)
tan
2
A
=
2
tan
A
1
−
tan
2
A
b)
cos
2
A
=
cos
2
A
−
sin
2
A
c)
tan
2
A
=
2
tan
A
1
+
tan
2
A
d)
sin
2
A
=
2
sin
2
A
cos
2
A
e)
sin
2
A
=
2
sin
A
cos
A
f)
cos
2
A
=
cos
2
A
+
sin
2
A
(i)
{c,a}
(ii)
{f,c,e}
(iii)
{d,b}
(iv)
{d,a,b}
(v)
{a,b,e}
Question
23
23.
Given that
4
sec
θ
=
5
, find
cot
θ
(i)
3
4
(ii)
4
3
(iii)
3
5
(iv)
5
3
(v)
4
5
Question
24
24.
In the given figure,
sin
C
=
(i)
1
(ii)
15
17
(iii)
13
17
(iv)
15
19
Question
25
25.
cos
20°
sin
4°
−
sin
70°
cos
86°
=
(i)
-1
(ii)
0
(iii)
1
(iv)
2
sin
4°
(v)
2
sin
20°
Assignment Key
1) (iii)
2) (iii)
3) (ii)
4) (iii)
5) (iv)
6) (v)
7) (iv)
8) (v)
9) (iii)
10) (ii)
11) (iv)
12) (v)
13) (i)
14) (v)
15) (ii)
16) (iv)
17) (iv)
18) (i)
19) (ii)
20) (iii)
21) (ii)
22) (v)
23) (ii)
24) (ii)
25) (ii)
