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)
tan
A
= tan
✕
A
b)
sin
(
A
+
B
)
=
sin
A
+
sin
B
c)
The cosecant of an angle is the reciprocal of the secant of the angle
d)
cos
(
A
+
B
)
=
cos
A
+
cos
B
e)
The cotangent of an angle is the reciprocal of the tangent of the angle.
f)
The cosine value of an angle is the reciprocal of the sine of the angle.
(i)
{b,e}
(ii)
{a,e}
(iii)
{c,d,e}
(iv)
{e}
(v)
{f,e}
Question
2
2.
If
sin
2
A
=
2
sin
A
, then
A
=
(i)
30°
(ii)
45°
(iii)
0°
(iv)
60°
(v)
90°
Question
3
3.
If
sin
(
B
+
C
)
=
1
2
√
3
and
sin
(
B
−
C
)
=
1
2
,
find
B
&
C
(i)
B
=
43°
,
C
=
13°
(ii)
B
=
47°
,
C
=
17°
(iii)
B
=
44°
,
C
=
14°
(iv)
B
=
45°
,
C
=
15°
(v)
B
=
46°
,
C
=
16°
Question
4
4.
If
tan
(
D
+
E
)
=
√
3
and
tan
(
D
−
E
)
=
√
1
3
,
find
D
&
E
(i)
D
=
47°
,
E
=
17°
(ii)
D
=
44°
,
E
=
14°
(iii)
D
=
43°
,
E
=
13°
(iv)
D
=
46°
,
E
=
16°
(v)
D
=
45°
,
E
=
15°
Question
5
5.
sin
90°
cos
0°
+
cos
90°
sin
0°
=
(i)
1
(ii)
0
(iii)
(
−
1
)
(iv)
3
(v)
2
Question
6
6.
In
△IJK
, right angled at
J
,
if
tan
I
=
4
5
,
find
sin
I
cos
K
+
cos
I
sin
K
(i)
5
41
√
41
(ii)
4
41
√
41
(iii)
1
5
√
41
(iv)
1
4
√
41
(v)
1
Question
7
7.
In
△JKL
, right angled at
K
,
if
tan
J
=
1
2
,
find
cos
J
cos
L
−
sin
J
sin
L
(i)
2
5
√
5
(ii)
√
5
(iii)
0
(iv)
1
5
√
5
(v)
1
2
√
5
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)
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
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)
cos
A
cos
B
+
sin
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
66°
=
(i)
cos
48°
cos
18°
+
sin
48°
sin
18°
(ii)
sin
48°
cos
18°
+
cos
48°
sin
18°
(iii)
cos
48°
cos
18°
−
sin
48°
sin
18°
(iv)
sin
48°
cos
18°
−
cos
48°
sin
18°
Question
15
15.
sin
36°
=
(i)
sin
42°
cos
6°
−
cos
42°
sin
6°
(ii)
sin
42°
cos
6°
+
cos
42°
sin
6°
(iii)
cos
42°
cos
6°
−
sin
42°
sin
6°
(iv)
cos
42°
cos
6°
+
sin
42°
sin
6°
Question
16
16.
cos
128°
=
(i)
cos
72°
cos
56°
−
sin
72°
sin
56°
(ii)
sin
72°
cos
56°
−
cos
72°
sin
56°
(iii)
cos
72°
cos
56°
+
sin
72°
sin
56°
(iv)
sin
72°
cos
56°
+
cos
72°
sin
56°
Question
17
17.
cos
40°
=
(i)
cos
64°
cos
24°
+
sin
64°
sin
24°
(ii)
cos
64°
cos
24°
−
sin
64°
sin
24°
(iii)
sin
64°
cos
24°
+
cos
64°
sin
24°
(iv)
sin
64°
cos
24°
−
cos
64°
sin
24°
Question
18
18.
tan
40°
=
(i)
tan
32°
−
tan
8°
1
+
tan
32°
tan
8°
(ii)
tan
32°
+
tan
8°
1
−
tan
32°
tan
8°
(iii)
tan
32°
+
tan
8°
1
+
tan
32°
tan
8°
(iv)
tan
32°
−
tan
8°
1
−
tan
32°
tan
8°
Question
19
19.
tan
24°
=
(i)
tan
48°
−
tan
24°
1
−
tan
48°
tan
24°
(ii)
tan
48°
+
tan
24°
1
+
tan
48°
tan
24°
(iii)
tan
48°
−
tan
24°
1
+
tan
48°
tan
24°
(iv)
tan
48°
+
tan
24°
1
−
tan
48°
tan
24°
Question
20
20.
Which of the following are true?
a)
sin
2
A
=
2
sin
A
cos
A
b)
sin
2
A
=
2
sin
2
A
cos
2
A
c)
tan
2
A
=
2
tan
A
1
+
tan
2
A
d)
cos
2
A
=
cos
2
A
+
sin
2
A
e)
tan
2
A
=
2
tan
A
1
−
tan
2
A
f)
cos
2
A
=
cos
2
A
−
sin
2
A
(i)
{b,a}
(ii)
{d,b,f}
(iii)
{c,a,e}
(iv)
{a,e,f}
(v)
{c,e}
Question
21
21.
Which of the following are true?
a)
sin
90°
=
2
sin
45°
cos
45°
b)
tan
90°
=
2
tan
45°
1
+
tan
2
45°
c)
cos
90°
=
cos
2
45°
+
sin
2
45°
d)
tan
90°
=
2
tan
45°
1
−
tan
2
45°
e)
sin
90°
=
2
sin
2
45°
cos
2
45°
f)
cos
90°
=
cos
2
45°
−
sin
2
45°
(i)
{c,d}
(ii)
{e,b,f}
(iii)
{c,a,d}
(iv)
{a,d,f}
(v)
{b,a}
Question
22
22.
Find the value of
(
1
+
sin
θ
)
(
cos
θ
)
+
(
cos
θ
)
(
1
+
sin
θ
)
(i)
2
sec
θ
(ii)
2
sin
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)
0.5840 m
(iv)
0.6840 m
Question
24
24.
Find the length of the chord of the unit circle subtending an angle of 116° at the centre
(i)
1.7400
(ii)
1.6900
(iii)
1.5900
(iv)
1.7900
Question
25
25.
Find the area of the right angled triangle with hypotenuse 5 cm and one of the acute angle being 62°
(i)
4.1815 cm
(ii)
6.1815 cm
(iii)
5.1815 cm
(iv)
7.1815 cm
Question
26
26.
Find the area of an isosceles triangle with base 6 cm and vertical angle 59°
(i)
15.9067 cm
(ii)
17.9067 cm
(iii)
16.9067 cm
(iv)
14.9067 cm
Question
27
27.
If
V
,
W
and
X
are the interior angles of a triangle, then
sin
(
V + W
2
)
=
(i)
sin
X
(ii)
cos
(
V
2
)
(iii)
sin
(
V
2
)
(iv)
cos
(
X
2
)
(v)
sin
(
X
2
)
Question
28
28.
Which of the following are true?
a)
sin
33°
=
cos
57°
b)
sin
56°
=
cos
34°
c)
tan
57°
=
cot
33°
d)
sin
26°
=
cos
26°
e)
cos
55°
=
sin
55°
f)
sec
36°
=
cosec
54°
g)
sin
49°
=
cos
41°
(i)
{d,e,c}
(ii)
{e,b}
(iii)
{d,f,g}
(iv)
{a,b,c,f,g}
(v)
{d,a}
Question
29
29.
Which of the following are true?
a)
sec
0°
is not defined
b)
tan
90°
is not defined
c)
cot
90°
is not defined
d)
cosec
0°
is not defined
e)
sec
90°
is not defined
f)
cot
0°
is not defined
g)
cosec
90°
is not defined
h)
tan
0°
is not defined
(i)
{a,b}
(ii)
{c,d}
(iii)
{b,d,e,f}
(iv)
{g,h,e}
(v)
{a,f,b}
Question
30
30.
Which of the following are true?
a)
tan
θ
=
1
cot
θ
b)
sec
θ
=
1
cos
θ
c)
cot
θ
=
1
sec
θ
d)
cos
θ
=
1
cosec
θ
e)
sec
θ
=
1
sin
θ
f)
cosec
θ
=
1
sin
θ
(i)
{e,c,f}
(ii)
{c,a}
(iii)
{a,b,f}
(iv)
{d,a,b}
(v)
{d,b}
Question
31
31.
Which of the following are true?
a)
sin
0°
=
1
b)
tan
90°
=
1
c)
cos
0°
=
1
d)
sin
45°
=
1
e)
sin
90°
=
1
f)
cos
90°
=
1
g)
tan
0°
=
1
h)
cos
45°
=
1
(i)
{b,e}
(ii)
{d,f,c}
(iii)
{a,c}
(iv)
{c,e}
(v)
{g,e,c}
Question
32
32.
Which of the following are true?
a)
sin
45°
=
0
b)
cos
45°
=
0
c)
sin
0°
=
0
d)
cos
90°
=
0
e)
tan
0°
=
0
f)
tan
90°
=
0
g)
cos
0°
=
0
h)
sin
90°
=
0
(i)
{f,g,e}
(ii)
{a,c}
(iii)
{h,c,d}
(iv)
{c,d,e}
(v)
{b,d}
Assignment Key
1) (iv)
2) (iii)
3) (iv)
4) (v)
5) (i)
6) (v)
7) (iii)
8) (iv)
9) (iv)
10) (ii)
11) (iii)
12) (iii)
13) (i)
14) (ii)
15) (i)
16) (i)
17) (i)
18) (ii)
19) (iii)
20) (iv)
21) (iv)
22) (i)
23) (iv)
24) (ii)
25) (iii)
26) (i)
27) (iv)
28) (iv)
29) (iii)
30) (iii)
31) (iv)
32) (iv)
