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
H
= tan
✕
H
b)
The cotangent of an angle is the reciprocal of the tangent of the angle.
c)
cos
(
H
+
I
)
=
cos
H
+
cos
I
d)
The cosecant of an angle is the reciprocal of the secant of the angle
e)
The cosine value of an angle is the reciprocal of the sine of the angle.
f)
sin
(
H
+
I
)
=
sin
H
+
sin
I
(i)
{c,b}
(ii)
{d,e,b}
(iii)
{b}
(iv)
{a,b}
(v)
{f,b}
Question
2
2.
If
sin
2
H
=
2
sin
H
, then
H
=
(i)
60°
(ii)
0°
(iii)
30°
(iv)
45°
(v)
90°
Question
3
3.
If
sin
(
H
+
I
)
=
1
2
√
3
and
sin
(
H
−
I
)
=
1
2
,
find
H
&
I
(i)
H
=
43°
,
I
=
13°
(ii)
H
=
46°
,
I
=
16°
(iii)
H
=
44°
,
I
=
14°
(iv)
H
=
47°
,
I
=
17°
(v)
H
=
45°
,
I
=
15°
Question
4
4.
If
tan
(
C
+
D
)
=
√
3
and
tan
(
C
−
D
)
=
√
1
3
,
find
C
&
D
(i)
C
=
43°
,
D
=
13°
(ii)
C
=
47°
,
D
=
17°
(iii)
C
=
45°
,
D
=
15°
(iv)
C
=
44°
,
D
=
14°
(v)
C
=
46°
,
D
=
16°
Question
5
5.
sin
60°
cos
90°
+
cos
60°
sin
90°
=
(i)
3
2
(ii)
1
(iii)
1
4
(iv)
(
−
1
2
)
(v)
1
2
Question
6
6.
In
△IJK
, right angled at
J
,
if
tan
I
=
5
8
,
find
sin
I
cos
K
+
cos
I
sin
K
(i)
1
8
√
89
(ii)
5
89
√
89
(iii)
1
5
√
89
(iv)
8
89
√
89
(v)
1
Question
7
7.
In
△BCD
, right angled at
C
,
if
tan
B
=
2
3
,
find
cos
B
cos
D
−
sin
B
sin
D
(i)
0
(ii)
2
13
√
13
(iii)
1
3
√
13
(iv)
1
2
√
13
(v)
3
13
√
13
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)
sin
A
cos
B
−
cos
A
sin
B
(iv)
cos
A
cos
B
+
sin
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)
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)
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
56°
=
(i)
cos
40°
cos
16°
+
sin
40°
sin
16°
(ii)
sin
40°
cos
16°
+
cos
40°
sin
16°
(iii)
sin
40°
cos
16°
−
cos
40°
sin
16°
(iv)
cos
40°
cos
16°
−
sin
40°
sin
16°
Question
15
15.
sin
8°
=
(i)
sin
56°
cos
48°
−
cos
56°
sin
48°
(ii)
sin
56°
cos
48°
+
cos
56°
sin
48°
(iii)
cos
56°
cos
48°
−
sin
56°
sin
48°
(iv)
cos
56°
cos
48°
+
sin
56°
sin
48°
Question
16
16.
cos
80°
=
(i)
sin
64°
cos
16°
+
cos
64°
sin
16°
(ii)
cos
64°
cos
16°
−
sin
64°
sin
16°
(iii)
sin
64°
cos
16°
−
cos
64°
sin
16°
(iv)
cos
64°
cos
16°
+
sin
64°
sin
16°
Question
17
17.
cos
7°
=
(i)
cos
21°
cos
14°
−
sin
21°
sin
14°
(ii)
sin
21°
cos
14°
+
cos
21°
sin
14°
(iii)
cos
21°
cos
14°
+
sin
21°
sin
14°
(iv)
sin
21°
cos
14°
−
cos
21°
sin
14°
Question
18
18.
tan
95°
=
(i)
tan
50°
−
tan
45°
1
−
tan
50°
tan
45°
(ii)
tan
50°
+
tan
45°
1
+
tan
50°
tan
45°
(iii)
tan
50°
−
tan
45°
1
+
tan
50°
tan
45°
(iv)
tan
50°
+
tan
45°
1
−
tan
50°
tan
45°
Question
19
19.
tan
40°
=
(i)
tan
45°
−
tan
5°
1
−
tan
45°
tan
5°
(ii)
tan
45°
+
tan
5°
1
+
tan
45°
tan
5°
(iii)
tan
45°
−
tan
5°
1
+
tan
45°
tan
5°
(iv)
tan
45°
+
tan
5°
1
−
tan
45°
tan
5°
Question
20
20.
Which of the following are true?
a)
sin
2
A
=
2
sin
2
A
cos
2
A
b)
tan
2
A
=
2
tan
A
1
+
tan
2
A
c)
tan
2
A
=
2
tan
A
1
−
tan
2
A
d)
sin
2
A
=
2
sin
A
cos
A
e)
cos
2
A
=
cos
2
A
+
sin
2
A
f)
cos
2
A
=
cos
2
A
−
sin
2
A
(i)
{a,c}
(ii)
{c,d,f}
(iii)
{b,d}
(iv)
{e,a,f}
(v)
{b,c,d}
Question
21
21.
Which of the following are true?
a)
tan
100°
=
2
tan
50°
1
+
tan
2
50°
b)
sin
100°
=
2
sin
2
50°
cos
2
50°
c)
tan
100°
=
2
tan
50°
1
−
tan
2
50°
d)
cos
100°
=
cos
2
50°
+
sin
2
50°
e)
sin
100°
=
2
sin
50°
cos
50°
f)
cos
100°
=
cos
2
50°
−
sin
2
50°
(i)
{b,e}
(ii)
{b,c,e}
(iii)
{c,e,f}
(iv)
{a,c}
(v)
{d,a,f}
Question
22
22.
Find the value of
(
1
+
sin
θ
)
(
cos
θ
)
+
(
cos
θ
)
(
1
+
sin
θ
)
(i)
2
cosec
θ
(ii)
2
sin
θ
(iii)
2
cos
θ
(iv)
2
sec
θ
Question
23
23.
Find the length of the side of a 14-sided regular polygon inscribed in a circle of radius 1 m
(i)
0.4328 m
(ii)
0.4828 m
(iii)
0.3328 m
(iv)
0.5328 m
Question
24
24.
Find the length of the chord of the unit circle subtending an angle of 152° at the centre
(i)
2.0406
(ii)
1.8406
(iii)
1.9906
(iv)
1.9406
Question
25
25.
Find the area of the right angled triangle with hypotenuse 3 cm and one of the acute angle being 70°
(i)
1.4462 cm
(ii)
0.4462 cm
(iii)
2.4462 cm
(iv)
3.4462 cm
Question
26
26.
Find the area of an isosceles triangle with base 8 cm and vertical angle 70°
(i)
23.8506 cm
(ii)
22.8506 cm
(iii)
21.8506 cm
(iv)
24.8506 cm
Question
27
27.
If
P
,
Q
and
R
are the interior angles of a triangle, then
sin
(
P + Q
2
)
=
(i)
sin
(
R
2
)
(ii)
sin
R
(iii)
cos
(
R
2
)
(iv)
cos
(
P
2
)
(v)
sin
(
P
2
)
Question
28
28.
Which of the following are true?
a)
sin
37°
=
cos
37°
b)
sin
52°
=
cos
38°
c)
sec
32°
=
cosec
58°
d)
sin
34°
=
cos
56°
e)
sin
51°
=
cos
39°
f)
tan
47°
=
cot
43°
g)
cos
38°
=
sin
38°
(i)
{a,g,d}
(ii)
{g,c}
(iii)
{a,b}
(iv)
{b,c,d,e,f}
(v)
{a,e,f}
Question
29
29.
Which of the following are true?
a)
cot
0°
is not defined
b)
cot
90°
is not defined
c)
tan
0°
is not defined
d)
cosec
0°
is not defined
e)
sec
0°
is not defined
f)
cosec
90°
is not defined
g)
sec
90°
is not defined
h)
tan
90°
is not defined
(i)
{a,d,g,h}
(ii)
{b,h,a}
(iii)
{e,f,g}
(iv)
{c,d}
(v)
{b,a}
Question
30
30.
Which of the following are true?
a)
cos
θ
=
1
cosec
θ
b)
tan
θ
=
1
cot
θ
c)
sec
θ
=
1
sin
θ
d)
cosec
θ
=
1
sin
θ
e)
sec
θ
=
1
cos
θ
f)
cot
θ
=
1
sec
θ
(i)
{b,d,e}
(ii)
{c,b,d}
(iii)
{a,b}
(iv)
{c,d}
(v)
{f,a,e}
Question
31
31.
Which of the following are true?
a)
cos
0°
=
1
b)
tan
0°
=
1
c)
sin
0°
=
1
d)
sin
90°
=
1
e)
tan
90°
=
1
f)
cos
45°
=
1
g)
cos
90°
=
1
h)
sin
45°
=
1
(i)
{b,a}
(ii)
{e,f,a}
(iii)
{c,d}
(iv)
{g,d,a}
(v)
{a,d}
Question
32
32.
Which of the following are true?
a)
tan
90°
=
0
b)
sin
90°
=
0
c)
sin
0°
=
0
d)
sin
45°
=
0
e)
cos
45°
=
0
f)
cos
0°
=
0
g)
tan
0°
=
0
h)
cos
90°
=
0
(i)
{d,e,h}
(ii)
{f,c,g}
(iii)
{c,g,h}
(iv)
{b,g}
(v)
{a,c}
Assignment Key
1) (iii)
2) (ii)
3) (v)
4) (iii)
5) (v)
6) (v)
7) (i)
8) (i)
9) (iii)
10) (i)
11) (iii)
12) (iii)
13) (iv)
14) (ii)
15) (i)
16) (ii)
17) (iii)
18) (iv)
19) (iii)
20) (ii)
21) (iii)
22) (iv)
23) (i)
24) (iv)
25) (i)
26) (ii)
27) (iii)
28) (iv)
29) (i)
30) (i)
31) (v)
32) (iii)
