EduSahara™ Worksheet
Name : Chapter Based Worksheet
Chapter : Trigonometrical Identities
Grade : ICSE Grade X
License : Non Commercial Use
Question
1
1.
Express
sin
θ
in terms of
cos
θ
(i)
cos
θ
√
1
−
cos
2
θ
(ii)
1
cos
θ
(iii)
1
√
1
−
cos
2
θ
(iv)
√
1
−
cos
2
θ
(v)
√
1
−
cos
2
θ
cos
θ
Question
2
2.
Express
cot
θ
in terms of
cosec
θ
(i)
1
√
cosec
2
θ
−
1
(ii)
cosec
θ
√
cosec
2
θ
−
1
(iii)
√
cosec
2
θ
−
1
(iv)
√
cosec
2
θ
−
1
cosec
θ
(v)
1
cosec
θ
Question
3
3.
cos
42°
sin
48°
=
(i)
tan
48°
(ii)
0
(iii)
1
(iv)
tan
42°
(v)
-1
Question
4
4.
Find the value of
tan
(50.1)°
From Table of Natural Tangents
x°
0'
6'
12'
18'
24'
30'
36'
42'
48'
54'
1'
2'
3'
4'
5'
50
1.1918
1.1960
1.2002
1.2045
1.2088
1.2131
1.2174
1.2218
1.2261
1.2305
7
14
22
29
36
(i)
1.1956
(ii)
1.1963
(iii)
1.196
(iv)
1.1964
(v)
1.1957
Question
5
5.
Given
cosec
N
=
5
,
find
cot
N
(i)
1
5
(ii)
2
√
6
(iii)
2
5
√
6
(iv)
1
12
√
6
(v)
5
12
√
6
Question
6
6.
sin
25°
cos
65°
+
cos
25°
sin
65°
sin
60°
cos
30°
+
cos
60°
sin
30°
=
(i)
2
(ii)
undefined
(iii)
-1
(iv)
0
(v)
1
Question
7
7.
cot
30°
=
(i)
√
3
(ii)
3
(iii)
√
5
(iv)
√
1
3
(v)
4
√
3
Question
8
8.
In
△HIJ
, right angled at
I
,
if
HI = 24 cm
and
IJ = 10 cm
,
find
sin
J
(i)
10
13
(ii)
4
5
(iii)
14
13
(iv)
12
11
(v)
12
13
Question
9
9.
Which of the following are true?
a)
cos
(
90
−
θ
)
=
cos
θ
b)
cosec
(
90
−
θ
)
=
sec
θ
c)
sec
(
90
−
θ
)
=
cosec
θ
d)
tan
(
90
−
θ
)
=
−
tan
θ
e)
cot
(
90
−
θ
)
=
tan
θ
f)
cos
(
90
−
θ
)
=
cot
θ
(i)
{d,c}
(ii)
{a,b}
(iii)
{d,b,c}
(iv)
{f,a,e}
(v)
{b,c,e}
Question
10
10.
Given
sin
B
=
4
5
,
find
tan
B
(i)
5
3
(ii)
3
4
(iii)
5
4
(iv)
4
3
(v)
3
5
Question
11
11.
The value of
cosec
136°
in terms of an angle between
0°
and
90°
is
(i)
−
cosec
46°
(ii)
−
sec
46°
(iii)
sec
46°
(iv)
cosec
46°
Question
12
12.
If
cos
4
x
=
sin
(
(
x
+
30
)
)
, then
x
=
(i)
13
(ii)
12
(iii)
10
(iv)
11
(v)
14
Question
13
13.
If
tan
θ
=
8
9
, find
(
1
+
cos
θ
)
(
1
−
cos
θ
)
(
1
+
sin
θ
)
(
1
−
sin
θ
)
(i)
64
83
(ii)
64
81
(iii)
64
79
(iv)
62
81
(v)
22
27
Question
14
14.
Find angle
θ
such that
tan
θ
=
1.264
From Table of Natural Tangents
x°
0'
6'
12'
18'
24'
30'
36'
42'
48'
54'
1'
2'
3'
4'
5'
51
1.2349
1.2393
1.2437
1.2484
1.2527
1.2572
1.2617
1.2662
1.2708
1.2753
8
15
23
30
38
(i)
51
°
39
'
(ii)
51
°
49
'
(iii)
51
°
29
'
(iv)
51
°
34
'
(v)
51
°
44
'
Question
15
15.
The value of
sin
172°
in terms of an angle between
0°
and
90°
is
(i)
sin
82°
(ii)
−
sin
82°
(iii)
−
cos
82°
(iv)
cos
82°
Question
16
16.
Find the value of
cos
(51.7)°
From Table of Natural Cosines
x°
0'
6'
12'
18'
24'
30'
36'
42'
48'
54'
1'
2'
3'
4'
5'
51
0.6293
0.6280
0.6266
0.6252
0.6239
0.6225
0.6211
0.6198
0.6184
0.9170
2
5
7
9
12
(i)
0.6194
(ii)
0.6195
(iii)
0.6201
(iv)
0.6198
(v)
0.6202
Question
17
17.
In the given figure, △JKL is a right angle triangle with ∠L = 90° and KL = 16 cm. R is the mid-point of JL. Find the length of the altitude from L to JK.
(i)
16
cm
(ii)
8
cm
(iii)
4
√
12
cm
(iv)
16
√
3
cm
(v)
8
√
2
cm
Question
18
18.
In the given figure, △HIJ is right angled at I. If IJ = 10 cm and ∠J = 45°, find HI and HJ
(i)
11
cm
&
20
cm
(ii)
10
cm
&
10
√
2
cm
(iii)
11
cm
&
23
cm
(iv)
11
cm
&
10
√
2
cm
(v)
9
cm
&
23
cm
Question
19
19.
If
sin
5
x
=
cos
(
(
x
+
48
)
)
, then
x
=
(i)
8
(ii)
7
(iii)
6
(iv)
4
(v)
10
Question
20
20.
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)
sin
2
θ
−
cos
2
θ
=
1
,
0 ≤ θ ≤ 90°
e)
cosec
2
θ
+
cot
2
θ
=
1
,
0 ≤ θ ≤ 90°
f)
sec
2
θ
−
tan
2
θ
=
1
,
0 ≤ θ ≤ 90°
(i)
{b,c,f}
(ii)
{e,a,f}
(iii)
{d,b,c}
(iv)
{d,c}
(v)
{a,b}
Question
21
21.
cot
35°
−
tan
55°
=
(i)
-1
(ii)
2
sin
55°
(iii)
2
sin
35°
(iv)
1
(v)
0
Question
22
22.
Given that
5
cos
θ
=
3
, find
sec
θ
(i)
3
4
(ii)
5
4
(iii)
5
3
(iv)
4
3
(v)
4
5
Question
23
23.
Given that
4
sec
θ
=
5
, find
cot
θ
(i)
4
5
(ii)
3
5
(iii)
4
3
(iv)
5
3
(v)
3
4
Question
24
24.
Which of the following are true?
a)
cos
(
360
−
θ
)
=
cos
θ
b)
sin
(
360
−
θ
)
=
−
sin
θ
c)
tan
(
360
−
θ
)
=
−
cot
θ
d)
cos
(
360
−
θ
)
=
sin
θ
e)
tan
(
360
−
θ
)
=
−
tan
θ
f)
sin
(
360
−
θ
)
=
−
cos
θ
(i)
{a,b,e}
(ii)
{c,a}
(iii)
{f,c,e}
(iv)
{d,a,b}
(v)
{d,b}
Question
25
25.
sec
J
=
(i)
1
tan
J
(ii)
1
sin
J
(iii)
1
cot
J
(iv)
1
cosec
J
(v)
1
cos
J
Assignment Key
1) (iv)
2) (iii)
3) (iii)
4) (iii)
5) (ii)
6) (v)
7) (i)
8) (v)
9) (v)
10) (iv)
11) (iii)
12) (ii)
13) (ii)
14) (i)
15) (iv)
16) (iv)
17) (v)
18) (ii)
19) (ii)
20) (i)
21) (v)
22) (iii)
23) (iii)
24) (i)
25) (v)
