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 cosine value of an angle is the reciprocal of the sine of the angle.
b)
tan
A
= tan
✕
A
c)
The cotangent of an angle is the reciprocal of the tangent of the angle.
d)
sin
(
A
+
B
)
=
sin
A
+
sin
B
e)
The cosecant of an angle is the reciprocal of the secant of the angle
f)
cos
(
A
+
B
)
=
cos
A
+
cos
B
(i)
{f,c}
(ii)
{b,c}
(iii)
{a,c}
(iv)
{c}
(v)
{d,e,c}
Question
2
2.
If
sin
2
E
=
2
sin
E
, then
E
=
(i)
0°
(ii)
45°
(iii)
60°
(iv)
90°
(v)
30°
Question
3
3.
If
sin
(
H
+
I
)
=
1
2
√
3
and
sin
(
H
−
I
)
=
1
2
,
find
H
&
I
(i)
H
=
45°
,
I
=
15°
(ii)
H
=
47°
,
I
=
17°
(iii)
H
=
44°
,
I
=
14°
(iv)
H
=
46°
,
I
=
16°
(v)
H
=
43°
,
I
=
13°
Question
4
4.
If
tan
(
C
+
D
)
=
√
3
and
tan
(
C
−
D
)
=
√
1
3
,
find
C
&
D
(i)
C
=
46°
,
D
=
16°
(ii)
C
=
45°
,
D
=
15°
(iii)
C
=
44°
,
D
=
14°
(iv)
C
=
47°
,
D
=
17°
(v)
C
=
43°
,
D
=
13°
Question
5
5.
sin
90°
cos
60°
+
cos
90°
sin
60°
=
(i)
3
2
(ii)
1
2
(iii)
1
(iv)
(
−
1
2
)
(v)
1
4
Question
6
6.
In
△MNO
, right angled at
N
,
if
tan
M
=
7
8
,
find
sin
M
cos
O
+
cos
M
sin
O
(i)
1
8
√
113
(ii)
1
7
√
113
(iii)
1
(iv)
7
113
√
113
(v)
8
113
√
113
Question
7
7.
In
△DEF
, right angled at
E
,
if
tan
D
=
1
3
,
find
cos
D
cos
F
−
sin
D
sin
F
(i)
√
10
(ii)
0
(iii)
1
10
√
10
(iv)
1
3
√
10
(v)
3
10
√
10
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)
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)
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
11
11.
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
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
112°
=
(i)
sin
72°
cos
40°
+
cos
72°
sin
40°
(ii)
cos
72°
cos
40°
−
sin
72°
sin
40°
(iii)
sin
72°
cos
40°
−
cos
72°
sin
40°
(iv)
cos
72°
cos
40°
+
sin
72°
sin
40°
Question
15
15.
sin
24°
=
(i)
sin
40°
cos
16°
+
cos
40°
sin
16°
(ii)
cos
40°
cos
16°
+
sin
40°
sin
16°
(iii)
sin
40°
cos
16°
−
cos
40°
sin
16°
(iv)
cos
40°
cos
16°
−
sin
40°
sin
16°
Question
16
16.
cos
105°
=
(i)
sin
56°
cos
49°
−
cos
56°
sin
49°
(ii)
sin
56°
cos
49°
+
cos
56°
sin
49°
(iii)
cos
56°
cos
49°
+
sin
56°
sin
49°
(iv)
cos
56°
cos
49°
−
sin
56°
sin
49°
Question
17
17.
cos
28°
=
(i)
cos
63°
cos
35°
+
sin
63°
sin
35°
(ii)
cos
63°
cos
35°
−
sin
63°
sin
35°
(iii)
sin
63°
cos
35°
−
cos
63°
sin
35°
(iv)
sin
63°
cos
35°
+
cos
63°
sin
35°
Question
18
18.
tan
128°
=
(i)
tan
72°
+
tan
56°
1
+
tan
72°
tan
56°
(ii)
tan
72°
−
tan
56°
1
−
tan
72°
tan
56°
(iii)
tan
72°
−
tan
56°
1
+
tan
72°
tan
56°
(iv)
tan
72°
+
tan
56°
1
−
tan
72°
tan
56°
Question
19
19.
tan
7°
=
(i)
tan
21°
−
tan
14°
1
−
tan
21°
tan
14°
(ii)
tan
21°
−
tan
14°
1
+
tan
21°
tan
14°
(iii)
tan
21°
+
tan
14°
1
+
tan
21°
tan
14°
(iv)
tan
21°
+
tan
14°
1
−
tan
21°
tan
14°
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)
cos
2
A
=
cos
2
A
+
sin
2
A
f)
tan
2
A
=
2
tan
A
1
+
tan
2
A
(i)
{e,b}
(ii)
{e,a,b}
(iii)
{a,b,d}
(iv)
{f,c,d}
(v)
{c,a}
Question
21
21.
Which of the following are true?
a)
tan
72°
=
2
tan
36°
1
−
tan
2
36°
b)
tan
72°
=
2
tan
36°
1
+
tan
2
36°
c)
cos
72°
=
cos
2
36°
+
sin
2
36°
d)
cos
72°
=
cos
2
36°
−
sin
2
36°
e)
sin
72°
=
2
sin
2
36°
cos
2
36°
f)
sin
72°
=
2
sin
36°
cos
36°
(i)
{c,a,d}
(ii)
{a,d,f}
(iii)
{c,d}
(iv)
{e,b,f}
(v)
{b,a}
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 13-sided regular polygon inscribed in a circle of radius 1 m
(i)
0.5168 m
(ii)
0.3668 m
(iii)
0.4668 m
(iv)
0.5668 m
Question
24
24.
Find the length of the chord of the unit circle subtending an angle of 105° at the centre
(i)
1.6368
(ii)
1.4868
(iii)
1.5868
(iv)
1.6868
Question
25
25.
Find the area of the right angled triangle with hypotenuse 4 cm and one of the acute angle being 42°
(i)
5.9777 cm
(ii)
4.9777 cm
(iii)
3.9777 cm
(iv)
2.9777 cm
Question
26
26.
Find the area of an isosceles triangle with base 8 cm and vertical angle 66°
(i)
26.6381 cm
(ii)
23.6381 cm
(iii)
25.6381 cm
(iv)
24.6381 cm
Question
27
27.
If
Q
,
R
and
S
are the interior angles of a triangle, then
sin
(
Q + R
2
)
=
(i)
sin
S
(ii)
cos
(
S
2
)
(iii)
sin
(
S
2
)
(iv)
cos
(
Q
2
)
(v)
sin
(
Q
2
)
Question
28
28.
Which of the following are true?
a)
sin
33°
=
cos
57°
b)
tan
59°
=
cot
31°
c)
sin
47°
=
cos
43°
d)
sin
30°
=
cos
60°
e)
sin
52°
=
cos
52°
f)
sec
43°
=
cosec
47°
g)
cos
36°
=
sin
36°
(i)
{e,d,f}
(ii)
{a,b,c,d,f}
(iii)
{g,b}
(iv)
{e,g,c}
(v)
{e,a}
Question
29
29.
Which of the following are true?
a)
cosec
90°
is not defined
b)
tan
0°
is not defined
c)
sec
90°
is not defined
d)
tan
90°
is not defined
e)
cosec
0°
is not defined
f)
cot
0°
is not defined
g)
sec
0°
is not defined
h)
cot
90°
is not defined
(i)
{a,f,c}
(ii)
{b,d}
(iii)
{g,h,e}
(iv)
{c,d,e,f}
(v)
{a,c}
Question
30
30.
Which of the following are true?
a)
sec
θ
=
1
sin
θ
b)
sec
θ
=
1
cos
θ
c)
cot
θ
=
1
sec
θ
d)
cos
θ
=
1
cosec
θ
e)
tan
θ
=
1
cot
θ
f)
cosec
θ
=
1
sin
θ
(i)
{c,b,e}
(ii)
{b,e,f}
(iii)
{d,a,f}
(iv)
{a,b}
(v)
{c,e}
Question
31
31.
Which of the following are true?
a)
sin
0°
=
1
b)
sin
90°
=
1
c)
cos
90°
=
1
d)
cos
45°
=
1
e)
sin
45°
=
1
f)
tan
0°
=
1
g)
tan
90°
=
1
h)
cos
0°
=
1
(i)
{a,b}
(ii)
{c,h}
(iii)
{f,h,b}
(iv)
{b,h}
(v)
{d,e,b}
Question
32
32.
Which of the following are true?
a)
sin
0°
=
0
b)
sin
45°
=
0
c)
tan
90°
=
0
d)
cos
45°
=
0
e)
tan
0°
=
0
f)
cos
90°
=
0
g)
cos
0°
=
0
h)
sin
90°
=
0
(i)
{h,a,e}
(ii)
{a,e,f}
(iii)
{b,a}
(iv)
{d,g,f}
(v)
{c,e}
Assignment Key
1) (iv)
2) (i)
3) (i)
4) (ii)
5) (ii)
6) (iii)
7) (ii)
8) (iii)
9) (i)
10) (ii)
11) (iv)
12) (iv)
13) (iii)
14) (i)
15) (iii)
16) (iv)
17) (i)
18) (iv)
19) (ii)
20) (iii)
21) (ii)
22) (ii)
23) (iii)
24) (iii)
25) (iii)
26) (iv)
27) (ii)
28) (ii)
29) (iv)
30) (ii)
31) (iv)
32) (ii)
