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)
cos
(
G
+
H
)
=
cos
G
+
cos
H
c)
The cosecant of an angle is the reciprocal of the secant of the angle
d)
sin
(
G
+
H
)
=
sin
G
+
sin
H
e)
The cosine value of an angle is the reciprocal of the sine of the angle.
f)
tan
G
= tan
✕
G
(i)
{d,e,a}
(ii)
{a}
(iii)
{f,a}
(iv)
{b,a}
(v)
{c,a}
Question
2
2.
If
sin
2
E
=
2
sin
E
, then
E
=
(i)
60°
(ii)
45°
(iii)
90°
(iv)
0°
(v)
30°
Question
3
3.
If
sin
(
F
+
G
)
=
1
2
√
3
and
sin
(
F
−
G
)
=
1
2
,
find
F
&
G
(i)
F
=
47°
,
G
=
17°
(ii)
F
=
44°
,
G
=
14°
(iii)
F
=
46°
,
G
=
16°
(iv)
F
=
43°
,
G
=
13°
(v)
F
=
45°
,
G
=
15°
Question
4
4.
If
tan
(
H
+
I
)
=
√
3
and
tan
(
H
−
I
)
=
√
1
3
,
find
H
&
I
(i)
H
=
45°
,
I
=
15°
(ii)
H
=
43°
,
I
=
13°
(iii)
H
=
44°
,
I
=
14°
(iv)
H
=
46°
,
I
=
16°
(v)
H
=
47°
,
I
=
17°
Question
5
5.
sin
45°
cos
60°
+
cos
45°
sin
60°
=
(i)
(
1
4
√
2
+
1
4
4
√
6
)
(ii)
(
1
4
√
5
+
1
4
√
6
)
(iii)
(
1
4
√
2
+
3
2
)
(iv)
(
1
4
√
2
+
1
4
√
6
)
(v)
(
1
4
√
-1
+
1
4
√
6
)
Question
6
6.
In
△JKL
, right angled at
K
,
if
tan
J
=
1
2
,
find
sin
J
cos
L
+
cos
J
sin
L
(i)
√
5
(ii)
1
(iii)
1
5
√
5
(iv)
2
5
√
5
(v)
1
2
√
5
Question
7
7.
In
△FGH
, right angled at
G
,
if
tan
F
=
3
5
,
find
cos
F
cos
H
−
sin
F
sin
H
(i)
0
(ii)
1
5
√
34
(iii)
3
34
√
34
(iv)
5
34
√
34
(v)
1
3
√
34
Question
8
8.
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
9
9.
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
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
56°
=
(i)
cos
48°
cos
8°
−
sin
48°
sin
8°
(ii)
sin
48°
cos
8°
+
cos
48°
sin
8°
(iii)
cos
48°
cos
8°
+
sin
48°
sin
8°
(iv)
sin
48°
cos
8°
−
cos
48°
sin
8°
Question
15
15.
sin
20°
=
(i)
sin
35°
cos
15°
−
cos
35°
sin
15°
(ii)
cos
35°
cos
15°
+
sin
35°
sin
15°
(iii)
sin
35°
cos
15°
+
cos
35°
sin
15°
(iv)
cos
35°
cos
15°
−
sin
35°
sin
15°
Question
16
16.
cos
72°
=
(i)
sin
48°
cos
24°
+
cos
48°
sin
24°
(ii)
cos
48°
cos
24°
+
sin
48°
sin
24°
(iii)
sin
48°
cos
24°
−
cos
48°
sin
24°
(iv)
cos
48°
cos
24°
−
sin
48°
sin
24°
Question
17
17.
cos
6°
=
(i)
sin
60°
cos
54°
−
cos
60°
sin
54°
(ii)
sin
60°
cos
54°
+
cos
60°
sin
54°
(iii)
cos
60°
cos
54°
−
sin
60°
sin
54°
(iv)
cos
60°
cos
54°
+
sin
60°
sin
54°
Question
18
18.
tan
80°
=
(i)
tan
72°
−
tan
8°
1
+
tan
72°
tan
8°
(ii)
tan
72°
+
tan
8°
1
−
tan
72°
tan
8°
(iii)
tan
72°
+
tan
8°
1
+
tan
72°
tan
8°
(iv)
tan
72°
−
tan
8°
1
−
tan
72°
tan
8°
Question
19
19.
tan
24°
=
(i)
tan
80°
+
tan
56°
1
+
tan
80°
tan
56°
(ii)
tan
80°
−
tan
56°
1
+
tan
80°
tan
56°
(iii)
tan
80°
+
tan
56°
1
−
tan
80°
tan
56°
(iv)
tan
80°
−
tan
56°
1
−
tan
80°
tan
56°
Question
20
20.
Which of the following are true?
a)
tan
2
A
=
2
tan
A
1
+
tan
2
A
b)
sin
2
A
=
2
sin
A
cos
A
c)
cos
2
A
=
cos
2
A
−
sin
2
A
d)
tan
2
A
=
2
tan
A
1
−
tan
2
A
e)
cos
2
A
=
cos
2
A
+
sin
2
A
f)
sin
2
A
=
2
sin
2
A
cos
2
A
(i)
{a,b}
(ii)
{e,b,c}
(iii)
{f,a,d}
(iv)
{e,c}
(v)
{b,c,d}
Question
21
21.
Which of the following are true?
a)
cos
48°
=
cos
2
24°
+
sin
2
24°
b)
sin
48°
=
2
sin
24°
cos
24°
c)
cos
48°
=
cos
2
24°
−
sin
2
24°
d)
sin
48°
=
2
sin
2
24°
cos
2
24°
e)
tan
48°
=
2
tan
24°
1
−
tan
2
24°
f)
tan
48°
=
2
tan
24°
1
+
tan
2
24°
(i)
{d,c}
(ii)
{a,b}
(iii)
{f,a,e}
(iv)
{b,c,e}
(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
cos
θ
(iii)
2
cosec
θ
(iv)
2
sin
θ
Question
23
23.
Find the length of the side of a 7-sided regular polygon inscribed in a circle of radius 1 m
(i)
0.9610 m
(ii)
0.7610 m
(iii)
0.8610 m
(iv)
0.9110 m
Question
24
24.
Find the length of the chord of the unit circle subtending an angle of 133° at the centre
(i)
1.9342
(ii)
1.8842
(iii)
1.7342
(iv)
1.8342
Question
25
25.
Find the area of the right angled triangle with hypotenuse 4 cm and one of the acute angle being 64°
(i)
4.1523 cm
(ii)
5.1523 cm
(iii)
2.1523 cm
(iv)
3.1523 cm
Question
26
26.
Find the area of an isosceles triangle with base 6 cm and vertical angle 52°
(i)
20.4540 cm
(ii)
18.4540 cm
(iii)
19.4540 cm
(iv)
17.4540 cm
Question
27
27.
If
R
,
S
and
T
are the interior angles of a triangle, then
sin
(
R + S
2
)
=
(i)
sin
(
T
2
)
(ii)
cos
(
R
2
)
(iii)
sin
(
R
2
)
(iv)
cos
(
T
2
)
(v)
sin
T
Question
28
28.
Which of the following are true?
a)
sin
59°
=
cos
31°
b)
sin
38°
=
cos
52°
c)
sec
40°
=
cosec
50°
d)
sin
34°
=
cos
56°
e)
sin
29°
=
cos
29°
f)
tan
56°
=
cot
34°
g)
cos
24°
=
sin
24°
(i)
{a,b,c,d,f}
(ii)
{e,d,f}
(iii)
{e,a}
(iv)
{g,b}
(v)
{e,g,c}
Question
29
29.
Which of the following are true?
a)
cot
0°
is not defined
b)
tan
90°
is not defined
c)
sec
0°
is not defined
d)
cosec
90°
is not defined
e)
sec
90°
is not defined
f)
cot
90°
is not defined
g)
cosec
0°
is not defined
h)
tan
0°
is not defined
(i)
{d,b}
(ii)
{c,g,a}
(iii)
{a,b,e,g}
(iv)
{c,a}
(v)
{f,h,e}
Question
30
30.
Which of the following are true?
a)
cosec
θ
=
1
sin
θ
b)
sec
θ
=
1
sin
θ
c)
cot
θ
=
1
sec
θ
d)
cos
θ
=
1
cosec
θ
e)
sec
θ
=
1
cos
θ
f)
tan
θ
=
1
cot
θ
(i)
{d,b,f}
(ii)
{b,a}
(iii)
{a,e,f}
(iv)
{c,e}
(v)
{c,a,e}
Question
31
31.
Which of the following are true?
a)
sin
0°
=
1
b)
tan
0°
=
1
c)
sin
45°
=
1
d)
cos
45°
=
1
e)
tan
90°
=
1
f)
cos
0°
=
1
g)
cos
90°
=
1
h)
sin
90°
=
1
(i)
{f,h}
(ii)
{b,h}
(iii)
{a,f}
(iv)
{c,d,f}
(v)
{e,h,f}
Question
32
32.
Which of the following are true?
a)
sin
0°
=
0
b)
tan
90°
=
0
c)
cos
45°
=
0
d)
tan
0°
=
0
e)
cos
90°
=
0
f)
sin
90°
=
0
g)
sin
45°
=
0
h)
cos
0°
=
0
(i)
{c,d}
(ii)
{b,a}
(iii)
{h,a,d}
(iv)
{a,d,e}
(v)
{f,g,e}
Assignment Key
1) (ii)
2) (iv)
3) (v)
4) (i)
5) (iv)
6) (ii)
7) (i)
8) (i)
9) (ii)
10) (iv)
11) (i)
12) (i)
13) (ii)
14) (ii)
15) (i)
16) (iv)
17) (iv)
18) (ii)
19) (ii)
20) (v)
21) (iv)
22) (i)
23) (iii)
24) (iv)
25) (iv)
26) (ii)
27) (iv)
28) (i)
29) (iii)
30) (iii)
31) (i)
32) (iv)
