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)
The cotangent of an angle is the reciprocal of the tangent of the angle.
b)
sin
(
B
+
C
)
=
sin
B
+
sin
C
c)
The cosine value of an angle is the reciprocal of the sine of the angle.
d)
cos
(
B
+
C
)
=
cos
B
+
cos
C
e)
tan
B
= tan
✕
B
f)
The cosecant of an angle is the reciprocal of the secant of the angle
(i)
{c,a}
(ii)
{a}
(iii)
{f,a}
(iv)
{b,a}
(v)
{d,e,a}
Question
2
2.
If
sin
2
G
=
2
sin
G
, then
G
=
(i)
30°
(ii)
45°
(iii)
0°
(iv)
60°
(v)
90°
Question
3
3.
If
sin
(
F
+
G
)
=
1
2
√
3
and
sin
(
F
−
G
)
=
1
2
,
find
F
&
G
(i)
F
=
44°
,
G
=
14°
(ii)
F
=
47°
,
G
=
17°
(iii)
F
=
46°
,
G
=
16°
(iv)
F
=
45°
,
G
=
15°
(v)
F
=
43°
,
G
=
13°
Question
4
4.
If
tan
(
F
+
G
)
=
√
3
and
tan
(
F
−
G
)
=
√
1
3
,
find
F
&
G
(i)
F
=
44°
,
G
=
14°
(ii)
F
=
45°
,
G
=
15°
(iii)
F
=
47°
,
G
=
17°
(iv)
F
=
46°
,
G
=
16°
(v)
F
=
43°
,
G
=
13°
Question
5
5.
sin
0°
cos
90°
+
cos
0°
sin
90°
=
(i)
0
(ii)
4
(iii)
(
−
1
)
(iv)
1
(v)
2
Question
6
6.
In
△MNO
, right angled at
N
,
if
tan
M
=
6
7
,
find
sin
M
cos
O
+
cos
M
sin
O
(i)
7
85
√
85
(ii)
6
85
√
85
(iii)
1
(iv)
1
6
√
85
(v)
1
7
√
85
Question
7
7.
In
△CDE
, right angled at
D
,
if
tan
C
=
3
7
,
find
cos
C
cos
E
−
sin
C
sin
E
(i)
7
58
√
58
(ii)
3
58
√
58
(iii)
0
(iv)
1
3
√
58
(v)
1
7
√
58
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)
cos
A
cos
B
+
sin
A
sin
B
(iv)
sin
A
cos
B
+
cos
A
sin
B
Question
9
9.
sin
(
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
10
10.
cos
(
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
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
42°
=
(i)
sin
36°
cos
6°
+
cos
36°
sin
6°
(ii)
cos
36°
cos
6°
+
sin
36°
sin
6°
(iii)
cos
36°
cos
6°
−
sin
36°
sin
6°
(iv)
sin
36°
cos
6°
−
cos
36°
sin
6°
Question
15
15.
sin
8°
=
(i)
cos
16°
cos
8°
−
sin
16°
sin
8°
(ii)
sin
16°
cos
8°
+
cos
16°
sin
8°
(iii)
sin
16°
cos
8°
−
cos
16°
sin
8°
(iv)
cos
16°
cos
8°
+
sin
16°
sin
8°
Question
16
16.
cos
32°
=
(i)
sin
24°
cos
8°
−
cos
24°
sin
8°
(ii)
cos
24°
cos
8°
−
sin
24°
sin
8°
(iii)
cos
24°
cos
8°
+
sin
24°
sin
8°
(iv)
sin
24°
cos
8°
+
cos
24°
sin
8°
Question
17
17.
cos
15°
=
(i)
sin
35°
cos
20°
−
cos
35°
sin
20°
(ii)
sin
35°
cos
20°
+
cos
35°
sin
20°
(iii)
cos
35°
cos
20°
+
sin
35°
sin
20°
(iv)
cos
35°
cos
20°
−
sin
35°
sin
20°
Question
18
18.
tan
77°
=
(i)
tan
63°
+
tan
14°
1
+
tan
63°
tan
14°
(ii)
tan
63°
−
tan
14°
1
−
tan
63°
tan
14°
(iii)
tan
63°
−
tan
14°
1
+
tan
63°
tan
14°
(iv)
tan
63°
+
tan
14°
1
−
tan
63°
tan
14°
Question
19
19.
tan
30°
=
(i)
tan
42°
−
tan
12°
1
+
tan
42°
tan
12°
(ii)
tan
42°
+
tan
12°
1
+
tan
42°
tan
12°
(iii)
tan
42°
−
tan
12°
1
−
tan
42°
tan
12°
(iv)
tan
42°
+
tan
12°
1
−
tan
42°
tan
12°
Question
20
20.
Which of the following are true?
a)
cos
2
A
=
cos
2
A
−
sin
2
A
b)
tan
2
A
=
2
tan
A
1
−
tan
2
A
c)
cos
2
A
=
cos
2
A
+
sin
2
A
d)
tan
2
A
=
2
tan
A
1
+
tan
2
A
e)
sin
2
A
=
2
sin
A
cos
A
f)
sin
2
A
=
2
sin
2
A
cos
2
A
(i)
{d,b}
(ii)
{c,a}
(iii)
{f,c,e}
(iv)
{d,a,b}
(v)
{a,b,e}
Question
21
21.
Which of the following are true?
a)
cos
28°
=
cos
2
14°
+
sin
2
14°
b)
sin
28°
=
2
sin
14°
cos
14°
c)
sin
28°
=
2
sin
2
14°
cos
2
14°
d)
tan
28°
=
2
tan
14°
1
+
tan
2
14°
e)
cos
28°
=
cos
2
14°
−
sin
2
14°
f)
tan
28°
=
2
tan
14°
1
−
tan
2
14°
(i)
{c,b,e}
(ii)
{d,a,f}
(iii)
{a,b}
(iv)
{c,e}
(v)
{b,e,f}
Question
22
22.
Find the value of
(
1
+
sin
θ
)
(
cos
θ
)
+
(
cos
θ
)
(
1
+
sin
θ
)
(i)
2
cosec
θ
(ii)
2
cos
θ
(iii)
2
sec
θ
(iv)
2
sin
θ
Question
23
23.
Find the length of the side of a 9-sided regular polygon inscribed in a circle of radius 1 m
(i)
0.7840 m
(ii)
0.7340 m
(iii)
0.6840 m
(iv)
0.5840 m
Question
24
24.
Find the length of the chord of the unit circle subtending an angle of 127° at the centre
(i)
1.8398
(ii)
1.6898
(iii)
1.7898
(iv)
1.8898
Question
25
25.
Find the area of the right angled triangle with hypotenuse 4 cm and one of the acute angle being 67°
(i)
1.8771 cm
(ii)
2.8771 cm
(iii)
3.8771 cm
(iv)
4.8771 cm
Question
26
26.
Find the area of an isosceles triangle with base 4 cm and vertical angle 64°
(i)
5.4010 cm
(ii)
7.4010 cm
(iii)
6.4010 cm
(iv)
8.4010 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
(
U
2
)
(iii)
cos
(
S
2
)
(iv)
sin
(
S
2
)
(v)
cos
(
U
2
)
Question
28
28.
Which of the following are true?
a)
cos
34°
=
sin
34°
b)
tan
29°
=
cot
61°
c)
sin
58°
=
cos
32°
d)
sec
52°
=
cosec
38°
e)
sin
26°
=
cos
64°
f)
sin
31°
=
cos
59°
g)
sin
20°
=
cos
20°
(i)
{a,g,d}
(ii)
{g,c}
(iii)
{b,c,d,e,f}
(iv)
{a,e,f}
(v)
{a,b}
Question
29
29.
Which of the following are true?
a)
cot
0°
is not defined
b)
cosec
90°
is not defined
c)
sec
0°
is not defined
d)
tan
0°
is not defined
e)
tan
90°
is not defined
f)
sec
90°
is not defined
g)
cosec
0°
is not defined
h)
cot
90°
is not defined
(i)
{b,g,a}
(ii)
{c,e}
(iii)
{b,a}
(iv)
{d,h,f}
(v)
{a,e,f,g}
Question
30
30.
Which of the following are true?
a)
sec
θ
=
1
sin
θ
b)
sec
θ
=
1
cos
θ
c)
tan
θ
=
1
cot
θ
d)
cot
θ
=
1
sec
θ
e)
cosec
θ
=
1
sin
θ
f)
cos
θ
=
1
cosec
θ
(i)
{b,c,e}
(ii)
{a,b}
(iii)
{f,a,e}
(iv)
{d,c}
(v)
{d,b,c}
Question
31
31.
Which of the following are true?
a)
sin
0°
=
1
b)
sin
90°
=
1
c)
sin
45°
=
1
d)
tan
90°
=
1
e)
cos
45°
=
1
f)
tan
0°
=
1
g)
cos
90°
=
1
h)
cos
0°
=
1
(i)
{d,e,b}
(ii)
{a,b}
(iii)
{c,h}
(iv)
{f,h,b}
(v)
{b,h}
Question
32
32.
Which of the following are true?
a)
cos
45°
=
0
b)
cos
90°
=
0
c)
sin
45°
=
0
d)
cos
0°
=
0
e)
sin
0°
=
0
f)
tan
90°
=
0
g)
sin
90°
=
0
h)
tan
0°
=
0
(i)
{c,e}
(ii)
{g,b,e}
(iii)
{a,b}
(iv)
{d,f,h}
(v)
{b,e,h}
Assignment Key
1) (ii)
2) (iii)
3) (iv)
4) (ii)
5) (iv)
6) (iii)
7) (iii)
8) (iv)
9) (iv)
10) (iv)
11) (ii)
12) (i)
13) (iv)
14) (i)
15) (iii)
16) (ii)
17) (iii)
18) (iv)
19) (i)
20) (v)
21) (v)
22) (iii)
23) (iii)
24) (iii)
25) (ii)
26) (iii)
27) (v)
28) (iii)
29) (v)
30) (i)
31) (v)
32) (v)
