EduSahara™ Worksheet
Name : Chapter Based Worksheet
Chapter : Trigonometrical Identities
Grade : ICSE Grade X
License : Non Commercial Use
Question
1
1.
In the given figure, △DFE is right angled at E. If DE = 13 cm and ∠F = 45°, find DF
(i)
26
cm
(ii)
13
2
√
12
cm
(iii)
13
cm
(iv)
13
√
2
cm
(v)
26
√
3
cm
Question
2
2.
The value of
tan
258°
in terms of an angle between
0°
and
90°
is
(i)
cot
78°
(ii)
tan
78°
(iii)
−
tan
78°
(iv)
−
cot
78°
Question
3
3.
Given
sec
N
=
2
3
√
3
,
find
cot
N
(i)
1
3
√
3
(ii)
√
3
(iii)
1
2
(iv)
1
2
√
3
(v)
2
Question
4
4.
In the given figure, △FGH is a right angle triangle with ∠H = 90° and GH = 14 cm. R is the mid-point of FH. Find RH
(i)
7
2
√
2
cm
(ii)
7
3
√
18
cm
(iii)
7
3
cm
(iv)
7
3
√
3
cm
(v)
7
cm
Question
5
5.
Given
cot
A
=
12
5
,
find
cosec
A
(i)
12
13
(ii)
5
13
(iii)
13
12
(iv)
13
5
(v)
5
12
Question
6
6.
Express
cosec
θ
in terms of
cot
θ
(i)
cot
θ
√
1
+
cot
2
θ
(ii)
1
cot
θ
(iii)
1
√
1
+
cot
2
θ
(iv)
√
1
+
cot
2
θ
(v)
√
1
+
cot
2
θ
cot
θ
Question
7
7.
cos
(
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
8
8.
In the given figure,
sec
D
=
(i)
DC
DB
(ii)
EC
ED
(iii)
BC
BD
(iv)
BD
CD
(v)
CB
CD
Question
9
9.
Given
cot
B
=
2
√
2
,
find
sec
B
(i)
1
4
√
2
(ii)
1
3
(iii)
2
3
√
2
(iv)
3
4
√
2
(v)
3
Question
10
10.
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)
{e,b}
(ii)
{c,e,d}
(iii)
{c,a,b}
(iv)
{c,a}
(v)
{a,b,d}
Question
11
11.
In the given figure, △DFE is right angled at E. If DE = 24 cm and ∠F = 60°, find EF
(i)
24
cm
(ii)
8
√
3
cm
(iii)
8
cm
(iv)
12
√
2
cm
(v)
8
√
18
cm
Question
12
12.
Given
sin
E
=
4
5
,
find
cosec
E
(i)
5
4
(ii)
3
4
(iii)
3
5
(iv)
5
3
(v)
4
3
Question
13
13.
The value of
sec
133°
in terms of an angle between
0°
and
90°
is
(i)
−
sec
43°
(ii)
sec
43°
(iii)
cosec
43°
(iv)
−
cosec
43°
Question
14
14.
In the given figure, △ACB is right angled at B. If AB = 8 cm and ∠C = 30°, find AD
(i)
1
cm
(ii)
4
cm
(iii)
3
cm
(iv)
5
cm
(v)
7
cm
Question
15
15.
Find the length of the side of a 6-sided regular polygon inscribed in a circle of radius 1 m
(i)
1.0500 m
(ii)
1.0000 m
(iii)
1.1000 m
(iv)
0.9000 m
Question
16
16.
For angle values from 0° to 90°, which of the following are true?
a)
The product of the sine and cosine values remains a constant
b)
The cotangent value of the angle increases
c)
The sum of the squares of the sine and cosine values remains a constant
d)
The tangent value of the angle increases
e)
The cosine value of the angle increases
f)
The sine value of the angle increases
(i)
{a,c}
(ii)
{b,d}
(iii)
{b,c,d}
(iv)
{e,a,f}
(v)
{c,d,f}
Question
17
17.
Express
sin
35°
in terms of
cot
35°
(i)
cot
35°
√
1
+
cot
2
35°
(ii)
√
1
+
cot
2
35°
cot
35°
(iii)
1
cot
35°
(iv)
√
1
+
cot
2
35°
(v)
1
√
1
+
cot
2
35°
Question
18
18.
Given
cos
F
=
4
7
√
3
,
find
cot
F
(i)
7
12
√
3
(ii)
4
√
3
(iii)
1
7
(iv)
7
(v)
1
12
√
3
Question
19
19.
In the given figure, △EFG is a right angle triangle with ∠G = 90° and FG = 13 cm. R is the mid-point of EG. Find ∠RFE using tables.
(i)
16
°
7
'
(ii)
19
°
7
'
(iii)
21
°
7
'
(iv)
22
°
7
'
(v)
17
°
7
'
Question
20
20.
sec
59°
cosec
71°
cosec
31°
sec
19°
=
(i)
0
(ii)
tan
71°
(iii)
-1
(iv)
1
(v)
tan
59°
Question
21
21.
The value of
sec
79°
in terms of an angle between
0°
and
90°
is
(i)
sec
79°
(ii)
cosec
79°
(iii)
−
cosec
79°
(iv)
−
sec
79°
Question
22
22.
The value of
cosec
45°
in terms of an angle between
0°
and
90°
is
(i)
−
sec
45°
(ii)
cosec
45°
(iii)
−
cosec
45°
(iv)
sec
45°
Question
23
23.
Which of the following are true?
a)
sec
(
90
−
θ
)
=
cosec
θ
b)
cos
(
90
−
θ
)
=
cos
θ
c)
cosec
(
90
−
θ
)
=
sec
θ
d)
cos
(
90
−
θ
)
=
cot
θ
e)
cot
(
90
−
θ
)
=
tan
θ
f)
tan
(
90
−
θ
)
=
−
tan
θ
(i)
{a,c,e}
(ii)
{d,c}
(iii)
{b,a}
(iv)
{f,b,e}
(v)
{d,a,c}
Question
24
24.
Express
tan
θ
in terms of
sin
θ
(i)
sin
θ
√
1
−
sin
2
θ
(ii)
√
1
−
sin
2
θ
sin
θ
(iii)
1
sin
θ
(iv)
1
√
1
−
sin
2
θ
(v)
√
1
−
sin
2
θ
Question
25
25.
In the given figure, △BDC is right angled at C. If BC = 15 cm and ∠D = 45°, find BE
(i)
15
4
√
12
cm
(ii)
15
2
cm
(iii)
15
2
√
2
cm
(iv)
15
√
3
cm
(v)
15
cm
Assignment Key
1) (iv)
2) (ii)
3) (ii)
4) (iv)
5) (iv)
6) (iv)
7) (i)
8) (iv)
9) (iv)
10) (v)
11) (ii)
12) (i)
13) (iv)
14) (ii)
15) (ii)
16) (v)
17) (v)
18) (ii)
19) (ii)
20) (iv)
21) (i)
22) (ii)
23) (i)
24) (i)
25) (iii)
