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)
sin
(
B
+
C
)
=
sin
B
+
sin
C
b)
The cotangent of an angle is the reciprocal of the tangent of the angle.
c)
The cosecant of an angle is the reciprocal of the secant of the angle
d)
cos
(
B
+
C
)
=
cos
B
+
cos
C
e)
The cosine value of an angle is the reciprocal of the sine of the angle.
f)
tan
B
= tan
✕
B
(i)
{a,b}
(ii)
{f,b}
(iii)
{b}
(iv)
{c,b}
(v)
{d,e,b}
Question
2
2.
If
sin
2
B
=
2
sin
B
, then
B
=
(i)
0°
(ii)
45°
(iii)
90°
(iv)
30°
(v)
60°
Question
3
3.
If
sin
(
E
+
F
)
=
1
2
√
3
and
sin
(
E
−
F
)
=
1
2
,
find
E
&
F
(i)
E
=
46°
,
F
=
16°
(ii)
E
=
43°
,
F
=
13°
(iii)
E
=
45°
,
F
=
15°
(iv)
E
=
47°
,
F
=
17°
(v)
E
=
44°
,
F
=
14°
Question
4
4.
If
tan
(
D
+
E
)
=
√
3
and
tan
(
D
−
E
)
=
√
1
3
,
find
D
&
E
(i)
D
=
45°
,
E
=
15°
(ii)
D
=
47°
,
E
=
17°
(iii)
D
=
43°
,
E
=
13°
(iv)
D
=
46°
,
E
=
16°
(v)
D
=
44°
,
E
=
14°
Question
5
5.
sin
90°
cos
45°
+
cos
90°
sin
45°
=
(i)
1
2
4
√
2
(ii)
1
2
√
4
(iii)
1
2
√
1
2
(iv)
1
2
√
2
(v)
1
Question
6
6.
In
△GHI
, right angled at
H
,
if
tan
G
=
1
2
,
find
sin
G
cos
I
+
cos
G
sin
I
(i)
2
5
√
5
(ii)
1
2
√
5
(iii)
1
5
√
5
(iv)
1
(v)
√
5
Question
7
7.
In
△GHI
, right angled at
H
,
if
tan
G
=
1
2
,
find
cos
G
cos
I
−
sin
G
sin
I
(i)
0
(ii)
√
5
(iii)
2
5
√
5
(iv)
1
2
√
5
(v)
1
5
√
5
Question
8
8.
sin
(
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
9
9.
sin
(
A
−
B
)
=
(i)
sin
A
cos
B
−
cos
A
sin
B
(ii)
cos
A
cos
B
−
sin
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)
sin
A
cos
B
−
cos
A
sin
B
(ii)
cos
A
cos
B
+
sin
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)
sin
A
cos
B
−
cos
A
sin
B
(ii)
cos
A
cos
B
−
sin
A
sin
B
(iii)
sin
A
cos
B
+
cos
A
sin
B
(iv)
cos
A
cos
B
+
sin
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
36°
=
(i)
cos
24°
cos
12°
+
sin
24°
sin
12°
(ii)
sin
24°
cos
12°
−
cos
24°
sin
12°
(iii)
sin
24°
cos
12°
+
cos
24°
sin
12°
(iv)
cos
24°
cos
12°
−
sin
24°
sin
12°
Question
15
15.
sin
8°
=
(i)
sin
56°
cos
48°
+
cos
56°
sin
48°
(ii)
cos
56°
cos
48°
+
sin
56°
sin
48°
(iii)
sin
56°
cos
48°
−
cos
56°
sin
48°
(iv)
cos
56°
cos
48°
−
sin
56°
sin
48°
Question
16
16.
cos
80°
=
(i)
sin
56°
cos
24°
+
cos
56°
sin
24°
(ii)
cos
56°
cos
24°
+
sin
56°
sin
24°
(iii)
sin
56°
cos
24°
−
cos
56°
sin
24°
(iv)
cos
56°
cos
24°
−
sin
56°
sin
24°
Question
17
17.
cos
40°
=
(i)
cos
50°
cos
10°
+
sin
50°
sin
10°
(ii)
sin
50°
cos
10°
+
cos
50°
sin
10°
(iii)
sin
50°
cos
10°
−
cos
50°
sin
10°
(iv)
cos
50°
cos
10°
−
sin
50°
sin
10°
Question
18
18.
tan
98°
=
(i)
tan
56°
−
tan
42°
1
+
tan
56°
tan
42°
(ii)
tan
56°
−
tan
42°
1
−
tan
56°
tan
42°
(iii)
tan
56°
+
tan
42°
1
+
tan
56°
tan
42°
(iv)
tan
56°
+
tan
42°
1
−
tan
56°
tan
42°
Question
19
19.
tan
12°
=
(i)
tan
36°
−
tan
24°
1
+
tan
36°
tan
24°
(ii)
tan
36°
+
tan
24°
1
−
tan
36°
tan
24°
(iii)
tan
36°
−
tan
24°
1
−
tan
36°
tan
24°
(iv)
tan
36°
+
tan
24°
1
+
tan
36°
tan
24°
Question
20
20.
Which of the following are true?
a)
sin
2
A
=
2
sin
A
cos
A
b)
cos
2
A
=
cos
2
A
−
sin
2
A
c)
sin
2
A
=
2
sin
2
A
cos
2
A
d)
tan
2
A
=
2
tan
A
1
+
tan
2
A
e)
tan
2
A
=
2
tan
A
1
−
tan
2
A
f)
cos
2
A
=
cos
2
A
+
sin
2
A
(i)
{a,b,e}
(ii)
{c,a}
(iii)
{f,c,e}
(iv)
{d,b}
(v)
{d,a,b}
Question
21
21.
Which of the following are true?
a)
cos
16°
=
cos
2
8°
+
sin
2
8°
b)
tan
16°
=
2
tan
8°
1
+
tan
2
8°
c)
tan
16°
=
2
tan
8°
1
−
tan
2
8°
d)
cos
16°
=
cos
2
8°
−
sin
2
8°
e)
sin
16°
=
2
sin
2
8°
cos
2
8°
f)
sin
16°
=
2
sin
8°
cos
8°
(i)
{c,d,f}
(ii)
{b,c,d}
(iii)
{a,c}
(iv)
{b,d}
(v)
{e,a,f}
Question
22
22.
Find the value of
(
1
+
sin
θ
)
(
cos
θ
)
+
(
cos
θ
)
(
1
+
sin
θ
)
(i)
2
sin
θ
(ii)
2
sec
θ
(iii)
2
cos
θ
(iv)
2
cosec
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 134° at the centre
(i)
1.9410
(ii)
1.8410
(iii)
1.8910
(iv)
1.7410
Question
25
25.
Find the area of the right angled triangle with hypotenuse 5 cm and one of the acute angle being 30°
(i)
4.4125 cm
(ii)
5.4125 cm
(iii)
6.4125 cm
(iv)
7.4125 cm
Question
26
26.
Find the area of an isosceles triangle with base 6 cm and vertical angle 64°
(i)
16.4023 cm
(ii)
15.4023 cm
(iii)
14.4023 cm
(iv)
13.4023 cm
Question
27
27.
If
Q
,
R
and
S
are the interior angles of a triangle, then
sin
(
Q + R
2
)
=
(i)
sin
(
Q
2
)
(ii)
cos
(
Q
2
)
(iii)
sin
S
(iv)
sin
(
S
2
)
(v)
cos
(
S
2
)
Question
28
28.
Which of the following are true?
a)
sin
43°
=
cos
43°
b)
cos
46°
=
sin
46°
c)
tan
21°
=
cot
69°
d)
sec
31°
=
cosec
59°
e)
sin
41°
=
cos
49°
f)
sin
49°
=
cos
41°
g)
sin
33°
=
cos
57°
(i)
{c,d,e,f,g}
(ii)
{b,d}
(iii)
{a,f,g}
(iv)
{a,c}
(v)
{a,b,e}
Question
29
29.
Which of the following are true?
a)
sec
90°
is not defined
b)
sec
0°
is not defined
c)
cosec
0°
is not defined
d)
tan
0°
is not defined
e)
tan
90°
is not defined
f)
cot
90°
is not defined
g)
cosec
90°
is not defined
h)
cot
0°
is not defined
(i)
{b,a}
(ii)
{a,c,e,h}
(iii)
{b,h,a}
(iv)
{f,g,e}
(v)
{d,c}
Question
30
30.
Which of the following are true?
a)
cot
θ
=
1
sec
θ
b)
sec
θ
=
1
sin
θ
c)
cosec
θ
=
1
sin
θ
d)
cos
θ
=
1
cosec
θ
e)
tan
θ
=
1
cot
θ
f)
sec
θ
=
1
cos
θ
(i)
{b,e}
(ii)
{a,c}
(iii)
{b,c,e}
(iv)
{c,e,f}
(v)
{d,a,f}
Question
31
31.
Which of the following are true?
a)
cos
45°
=
1
b)
sin
0°
=
1
c)
cos
90°
=
1
d)
sin
90°
=
1
e)
tan
0°
=
1
f)
cos
0°
=
1
g)
sin
45°
=
1
h)
tan
90°
=
1
(i)
{d,f}
(ii)
{a,d}
(iii)
{g,f,d}
(iv)
{b,f}
(v)
{c,e,d}
Question
32
32.
Which of the following are true?
a)
tan
90°
=
0
b)
sin
90°
=
0
c)
cos
45°
=
0
d)
tan
0°
=
0
e)
sin
45°
=
0
f)
cos
90°
=
0
g)
sin
0°
=
0
h)
cos
0°
=
0
(i)
{a,d}
(ii)
{c,e,g}
(iii)
{b,f}
(iv)
{d,f,g}
(v)
{h,d,f}
Assignment Key
1) (iii)
2) (i)
3) (iii)
4) (i)
5) (iv)
6) (iv)
7) (i)
8) (iv)
9) (i)
10) (iv)
11) (iv)
12) (i)
13) (iii)
14) (iii)
15) (iii)
16) (iv)
17) (i)
18) (iv)
19) (i)
20) (i)
21) (i)
22) (ii)
23) (iii)
24) (ii)
25) (ii)
26) (iii)
27) (v)
28) (i)
29) (ii)
30) (iv)
31) (i)
32) (iv)
