EduSahara™ Assignment
Name : Trigonometry Miscellaneous
Chapter : Trigonometrical Ratios
Grade : ICSE Grade IX
License : Non Commercial Use
Question
1
1.
Which of the following are true?
a)
cos
(
G
+
H
)
=
cos
G
+
cos
H
b)
The cotangent of an angle is the reciprocal of the tangent of the angle.
c)
The cosine value of an angle is the reciprocal of the sine of the angle.
d)
The cosecant of an angle is the reciprocal of the secant of the angle
e)
tan
G
= tan
✕
G
f)
sin
(
G
+
H
)
=
sin
G
+
sin
H
(i)
{b}
(ii)
{f,b}
(iii)
{c,b}
(iv)
{a,b}
(v)
{d,e,b}
Question
2
2.
If
sin
2
H
=
2
sin
H
, then
H
=
(i)
45°
(ii)
30°
(iii)
60°
(iv)
90°
(v)
0°
Question
3
3.
If
sin
(
G
+
H
)
=
1
2
√
3
and
sin
(
G
−
H
)
=
1
2
,
find
G
&
H
(i)
G
=
44°
,
H
=
14°
(ii)
G
=
46°
,
H
=
16°
(iii)
G
=
47°
,
H
=
17°
(iv)
G
=
45°
,
H
=
15°
(v)
G
=
43°
,
H
=
13°
Question
4
4.
If
tan
(
E
+
F
)
=
√
3
and
tan
(
E
−
F
)
=
√
1
3
,
find
E
&
F
(i)
E
=
43°
,
F
=
13°
(ii)
E
=
46°
,
F
=
16°
(iii)
E
=
45°
,
F
=
15°
(iv)
E
=
47°
,
F
=
17°
(v)
E
=
44°
,
F
=
14°
Question
5
5.
sin
45°
cos
30°
+
cos
45°
sin
30°
=
(i)
(
1
4
√
3
+
1
4
√
2
)
(ii)
(
1
4
√
6
+
1
4
4
√
2
)
(iii)
(
1
4
√
9
+
1
4
√
2
)
(iv)
(
1
4
√
6
+
1
4
√
2
)
(v)
(
1
4
√
6
+
1
2
)
Question
6
6.
In
△DEF
, right angled at
E
,
if
tan
D
=
3
4
,
find
sin
D
cos
F
+
cos
D
sin
F
(i)
3
5
(ii)
5
4
(iii)
1
(iv)
4
5
(v)
5
3
Question
7
7.
In
△IJK
, right angled at
J
,
if
tan
I
=
2
3
,
find
cos
I
cos
K
−
sin
I
sin
K
(i)
3
13
√
13
(ii)
0
(iii)
1
2
√
13
(iv)
2
13
√
13
(v)
1
3
√
13
Question
8
8.
sin
(
A
+
B
)
=
(i)
cos
A
cos
B
+
sin
A
sin
B
(ii)
sin
A
cos
B
+
cos
A
sin
B
(iii)
sin
A
cos
B
−
cos
A
sin
B
(iv)
cos
A
cos
B
−
sin
A
sin
B
Question
9
9.
sin
(
A
−
B
)
=
(i)
sin
A
cos
B
+
cos
A
sin
B
(ii)
sin
A
cos
B
−
cos
A
sin
B
(iii)
cos
A
cos
B
−
sin
A
sin
B
(iv)
cos
A
cos
B
+
sin
A
sin
B
Question
10
10.
cos
(
A
+
B
)
=
(i)
sin
A
cos
B
−
cos
A
sin
B
(ii)
sin
A
cos
B
+
cos
A
sin
B
(iii)
cos
A
cos
B
−
sin
A
sin
B
(iv)
cos
A
cos
B
+
sin
A
sin
B
Question
11
11.
cos
(
A
−
B
)
=
(i)
cos
A
cos
B
+
sin
A
sin
B
(ii)
cos
A
cos
B
−
sin
A
sin
B
(iii)
sin
A
cos
B
−
cos
A
sin
B
(iv)
sin
A
cos
B
+
cos
A
sin
B
Question
12
12.
tan
(
A
+
B
)
=
(i)
tan
A
−
tan
B
1
−
tan
A
tan
B
(ii)
tan
A
+
tan
B
1
+
tan
A
tan
B
(iii)
tan
A
−
tan
B
1
+
tan
A
tan
B
(iv)
tan
A
+
tan
B
1
−
tan
A
tan
B
Question
13
13.
tan
(
A
−
B
)
=
(i)
tan
A
+
tan
B
1
+
tan
A
tan
B
(ii)
tan
A
−
tan
B
1
+
tan
A
tan
B
(iii)
tan
A
−
tan
B
1
−
tan
A
tan
B
(iv)
tan
A
+
tan
B
1
−
tan
A
tan
B
Question
14
14.
sin
91°
=
(i)
cos
70°
cos
21°
+
sin
70°
sin
21°
(ii)
cos
70°
cos
21°
−
sin
70°
sin
21°
(iii)
sin
70°
cos
21°
+
cos
70°
sin
21°
(iv)
sin
70°
cos
21°
−
cos
70°
sin
21°
Question
15
15.
sin
56°
=
(i)
cos
64°
cos
8°
−
sin
64°
sin
8°
(ii)
sin
64°
cos
8°
−
cos
64°
sin
8°
(iii)
sin
64°
cos
8°
+
cos
64°
sin
8°
(iv)
cos
64°
cos
8°
+
sin
64°
sin
8°
Question
16
16.
cos
60°
=
(i)
sin
48°
cos
12°
−
cos
48°
sin
12°
(ii)
cos
48°
cos
12°
−
sin
48°
sin
12°
(iii)
sin
48°
cos
12°
+
cos
48°
sin
12°
(iv)
cos
48°
cos
12°
+
sin
48°
sin
12°
Question
17
17.
cos
48°
=
(i)
sin
60°
cos
12°
+
cos
60°
sin
12°
(ii)
cos
60°
cos
12°
−
sin
60°
sin
12°
(iii)
sin
60°
cos
12°
−
cos
60°
sin
12°
(iv)
cos
60°
cos
12°
+
sin
60°
sin
12°
Question
18
18.
tan
65°
=
(i)
tan
40°
−
tan
25°
1
+
tan
40°
tan
25°
(ii)
tan
40°
+
tan
25°
1
−
tan
40°
tan
25°
(iii)
tan
40°
−
tan
25°
1
−
tan
40°
tan
25°
(iv)
tan
40°
+
tan
25°
1
+
tan
40°
tan
25°
Question
19
19.
tan
5°
=
(i)
tan
45°
−
tan
40°
1
−
tan
45°
tan
40°
(ii)
tan
45°
+
tan
40°
1
−
tan
45°
tan
40°
(iii)
tan
45°
+
tan
40°
1
+
tan
45°
tan
40°
(iv)
tan
45°
−
tan
40°
1
+
tan
45°
tan
40°
Question
20
20.
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)
cos
2
A
=
cos
2
A
−
sin
2
A
d)
sin
2
A
=
2
sin
2
A
cos
2
A
e)
tan
2
A
=
2
tan
A
1
+
tan
2
A
f)
sin
2
A
=
2
sin
A
cos
A
(i)
{d,a,c}
(ii)
{e,b,f}
(iii)
{d,c}
(iv)
{b,a}
(v)
{a,c,f}
Question
21
21.
Which of the following are true?
a)
tan
70°
=
2
tan
35°
1
+
tan
2
35°
b)
cos
70°
=
cos
2
35°
−
sin
2
35°
c)
sin
70°
=
2
sin
35°
cos
35°
d)
cos
70°
=
cos
2
35°
+
sin
2
35°
e)
sin
70°
=
2
sin
2
35°
cos
2
35°
f)
tan
70°
=
2
tan
35°
1
−
tan
2
35°
(i)
{a,b}
(ii)
{d,c}
(iii)
{e,a,f}
(iv)
{b,c,f}
(v)
{d,b,c}
Question
22
22.
Find the value of
(
1
+
sin
θ
)
(
cos
θ
)
+
(
cos
θ
)
(
1
+
sin
θ
)
(i)
2
sec
θ
(ii)
2
cosec
θ
(iii)
2
sin
θ
(iv)
2
cos
θ
Question
23
23.
Find the length of the side of a 14-sided regular polygon inscribed in a circle of radius 1 m
(i)
0.5328 m
(ii)
0.4328 m
(iii)
0.4828 m
(iv)
0.3328 m
Question
24
24.
Find the length of the chord of the unit circle subtending an angle of 134° at the centre
(i)
1.7410
(ii)
1.8410
(iii)
1.9410
(iv)
1.8910
Question
25
25.
Find the area of the right angled triangle with hypotenuse 7 cm and one of the acute angle being 55°
(i)
13.5124 cm
(ii)
11.5124 cm
(iii)
10.5124 cm
(iv)
12.5124 cm
Question
26
26.
Find the area of an isosceles triangle with base 6 cm and vertical angle 55°
(i)
19.2877 cm
(ii)
18.2877 cm
(iii)
16.2877 cm
(iv)
17.2877 cm
Question
27
27.
If
S
,
T
and
U
are the interior angles of a triangle, then
sin
(
S + T
2
)
=
(i)
sin
U
(ii)
sin
(
S
2
)
(iii)
cos
(
U
2
)
(iv)
sin
(
U
2
)
(v)
cos
(
S
2
)
Question
28
28.
Which of the following are true?
a)
sec
35°
=
cosec
55°
b)
sin
23°
=
cos
67°
c)
sin
51°
=
cos
39°
d)
sin
22°
=
cos
68°
e)
cos
21°
=
sin
21°
f)
sin
36°
=
cos
36°
g)
tan
58°
=
cot
32°
(i)
{e,a}
(ii)
{e,f,c}
(iii)
{f,b}
(iv)
{e,d,g}
(v)
{a,b,c,d,g}
Question
29
29.
Which of the following are true?
a)
cot
0°
is not defined
b)
sec
0°
is not defined
c)
cosec
90°
is not defined
d)
tan
90°
is not defined
e)
tan
0°
is not defined
f)
cosec
0°
is not defined
g)
sec
90°
is not defined
h)
cot
90°
is not defined
(i)
{c,d}
(ii)
{b,g,a}
(iii)
{a,d,f,g}
(iv)
{e,h,f}
(v)
{b,a}
Question
30
30.
Which of the following are true?
a)
cos
θ
=
1
cosec
θ
b)
sec
θ
=
1
sin
θ
c)
cosec
θ
=
1
sin
θ
d)
cot
θ
=
1
sec
θ
e)
sec
θ
=
1
cos
θ
f)
tan
θ
=
1
cot
θ
(i)
{d,a,f}
(ii)
{a,c}
(iii)
{c,e,f}
(iv)
{b,c,e}
(v)
{b,e}
Question
31
31.
Which of the following are true?
a)
tan
0°
=
1
b)
sin
0°
=
1
c)
cos
0°
=
1
d)
cos
90°
=
1
e)
cos
45°
=
1
f)
tan
90°
=
1
g)
sin
45°
=
1
h)
sin
90°
=
1
(i)
{a,c}
(ii)
{b,h}
(iii)
{f,h,c}
(iv)
{c,h}
(v)
{d,e,c}
Question
32
32.
Which of the following are true?
a)
tan
0°
=
0
b)
cos
90°
=
0
c)
sin
90°
=
0
d)
sin
45°
=
0
e)
cos
45°
=
0
f)
cos
0°
=
0
g)
sin
0°
=
0
h)
tan
90°
=
0
(i)
{d,b}
(ii)
{h,a,b}
(iii)
{c,a}
(iv)
{e,f,g}
(v)
{a,b,g}
Assignment Key
1) (i)
2) (v)
3) (iv)
4) (iii)
5) (iv)
6) (iii)
7) (ii)
8) (ii)
9) (ii)
10) (iii)
11) (i)
12) (iv)
13) (ii)
14) (iii)
15) (ii)
16) (ii)
17) (iv)
18) (ii)
19) (iv)
20) (v)
21) (iv)
22) (i)
23) (ii)
24) (ii)
25) (ii)
26) (iv)
27) (iii)
28) (v)
29) (iii)
30) (iii)
31) (iv)
32) (v)
