EduSahara™ Assignment
Name : Trigonometry Miscellaneous
Chapter : Trigonometry
Grade : SSC Grade X
License : Non Commercial Use
Question
1
1.
Which of the following are true?
a)
If
sin
D
= 0 , then
cos
D
= 1 or
cos
D
= -1
b)
The value of
tan
D
is always less than 1
c)
cos
D
is the abbrieviation for
cosec
D
d)
The value of
cot
D
is always less than 1
e)
The value of
sin
D
is always less than 1
(i)
{d,b,a}
(ii)
{b,a}
(iii)
{c,e}
(iv)
{a,e}
(v)
{c,e,a}
Question
2
2.
For angle values from 0° to 90°, which of the following are true?
a)
The tangent value of the angle increases
b)
The sine value of the angle increases
c)
The product of the sine and cosine values remains a constant
d)
The cosine value of the angle increases
e)
The sum of the squares of the sine and cosine values remains a constant
f)
The cotangent value of the angle increases
(i)
{f,c,e}
(ii)
{a,b,e}
(iii)
{c,a}
(iv)
{d,a,b}
(v)
{d,b}
Question
3
3.
Which of the following are true?
a)
The cosine value of an angle is the reciprocal of the sine of the angle.
b)
The cotangent of an angle is the reciprocal of the tangent of the angle.
c)
cos
(
E
+
F
)
=
cos
E
+
cos
F
d)
sin
(
E
+
F
)
=
sin
E
+
sin
F
e)
tan
E
= tan
✕
E
f)
The cosecant of an angle is the reciprocal of the secant of the angle
(i)
{b}
(ii)
{f,b}
(iii)
{d,e,b}
(iv)
{a,b}
(v)
{c,b}
Question
4
4.
Which of the following are true?
a)
cos
(
G
+
H
)
=
cos
G
+
cos
H
b)
tan
θ
=
cot
θ
for no value of
θ
c)
The value of
sin
θ
increases as
θ
increases from
0°
to
90°
d)
sin
θ
=
cos
θ
for all
θ
e)
sin
(
G
+
H
)
=
sin
G
+
sin
H
f)
tan
(
G
+
H
)
=
tan
G
+
tan
H
g)
The value of
cos
θ
increases as
θ
increases from
0°
to
90°
(i)
{b,c}
(ii)
{d,e,c}
(iii)
{c}
(iv)
{a,c}
(v)
{f,c}
Question
5
5.
Which of the following are true?
a)
sin
2
θ
−
cos
2
θ
=
1
,
0 ≤ θ ≤ 90°
b)
cosec
2
θ
+
cot
2
θ
=
1
,
0 ≤ θ ≤ 90°
c)
sec
2
θ
+
tan
2
θ
=
1
,
0 ≤ θ ≤ 90°
d)
sin
2
θ
+
cos
2
θ
=
1
,
0 ≤ θ ≤ 90°
e)
sec
2
θ
−
tan
2
θ
=
1
,
0 ≤ θ ≤ 90°
f)
cosec
2
θ
−
cot
2
θ
=
1
,
0 ≤ θ ≤ 90°
(i)
{c,a,f}
(ii)
{b,e}
(iii)
{b,d,e}
(iv)
{a,d}
(v)
{d,e,f}
Question
6
6.
If
sin
2
H
=
2
sin
H
, then
H
=
(i)
30°
(ii)
90°
(iii)
60°
(iv)
0°
(v)
45°
Question
7
7.
If
sin
(
C
+
D
)
=
1
2
√
3
and
sin
(
C
−
D
)
=
1
2
,
find
C
&
D
(i)
C
=
47°
,
D
=
17°
(ii)
C
=
44°
,
D
=
14°
(iii)
C
=
46°
,
D
=
16°
(iv)
C
=
43°
,
D
=
13°
(v)
C
=
45°
,
D
=
15°
Question
8
8.
If
tan
(
B
+
C
)
=
√
3
and
tan
(
B
−
C
)
=
√
1
3
,
find
B
&
C
(i)
B
=
44°
,
C
=
14°
(ii)
B
=
47°
,
C
=
17°
(iii)
B
=
43°
,
C
=
13°
(iv)
B
=
45°
,
C
=
15°
(v)
B
=
46°
,
C
=
16°
Question
9
9.
If
sin
4
x
=
cos
(
(
x
+
30
)
)
, then
x
=
(i)
11
(ii)
12
(iii)
15
(iv)
13
(v)
9
Question
10
10.
If
cos
6
x
=
sin
(
(
x
+
34
)
)
, then
x
=
(i)
5
(ii)
7
(iii)
11
(iv)
8
(v)
9
Question
11
11.
If
tan
4
x
=
cot
(
(
x
+
20
)
)
, then
x
=
(i)
14
(ii)
11
(iii)
13
(iv)
17
(v)
15
Question
12
12.
If
cot
8
x
=
tan
(
(
x
−
36
)
)
, then
x
=
(i)
15
(ii)
14
(iii)
11
(iv)
13
(v)
16
Question
13
13.
If
sec
8
x
=
cosec
(
(
x
−
9
)
)
, then
x
=
(i)
11
(ii)
14
(iii)
12
(iv)
10
(v)
9
Question
14
14.
If
cosec
4
x
=
sec
(
(
x
+
30
)
)
, then
x
=
(i)
9
(ii)
11
(iii)
15
(iv)
13
(v)
12
Question
15
15.
Which of the following are true?
a)
cos
θ
1
−
sin
θ
+
cos
θ
1
+
sin
θ
=
2
b)
(
sec
θ
−
tan
θ
)
2
=
1
+
sin
θ
1
−
sin
θ
c)
(
sec
θ
−
tan
θ
)
2
=
1
−
sin
θ
1
+
sin
θ
d)
1
+
sin
θ
cos
θ
+
cos
θ
1
+
sin
θ
=
2
sec
θ
e)
cos
θ
cosec
θ
+
1
+
cos
θ
cosec
θ
−
1
=
2
tan
θ
(i)
{a,c,d}
(ii)
{a,c}
(iii)
{a,b,e}
(iv)
{c,d,e}
(v)
{b,d}
Question
16
16.
Which of the following are true?
a)
cos
θ
1
+
sin
θ
=
1
−
sin
θ
cos
θ
b)
cos
3
θ
+
sin
3
θ
=
(
sin
θ
+
cos
θ
)
(
1
−
sin
θ
cos
θ
)
c)
sec
θ
1
+
cosec
θ
=
1
−
cosec
θ
sec
θ
d)
(
sin
θ
+
cos
θ
)
2
+
(
sin
θ
−
cos
θ
)
2
=
2
e)
(
sin
θ
+
cos
θ
)
2
=
1
+
sin
2
θ
f)
cos
3
θ
−
sin
3
θ
=
(
sin
θ
+
cos
θ
)
(
1
−
sin
θ
cos
θ
)
g)
(
sin
θ
−
cos
θ
)
2
=
1
+
sin
2
θ
(i)
{a,b,d,e}
(ii)
{f,b}
(iii)
{g,c,d}
(iv)
{c,a}
(v)
{f,e,a}
Question
17
17.
If
P
,
Q
and
R
are the interior angles of a triangle, then
sin
(
P + Q
2
)
=
(i)
sin
(
P
2
)
(ii)
sin
(
R
2
)
(iii)
sin
R
(iv)
cos
(
R
2
)
(v)
cos
(
P
2
)
Question
18
18.
Which of the following are true?
a)
sin
54°
=
cos
36°
b)
cos
37°
=
sin
37°
c)
sec
28°
=
cosec
62°
d)
sin
29°
=
cos
61°
e)
tan
23°
=
cot
67°
f)
sin
51°
=
cos
51°
g)
sin
58°
=
cos
32°
(i)
{f,c}
(ii)
{a,c,d,e,g}
(iii)
{b,a}
(iv)
{b,f,d}
(v)
{b,e,g}
Question
19
19.
Which of the following are true?
a)
cosec
90°
is not defined
b)
sec
90°
is not defined
c)
cosec
0°
is not defined
d)
cot
0°
is not defined
e)
tan
90°
is not defined
f)
tan
0°
is not defined
g)
sec
0°
is not defined
h)
cot
90°
is not defined
(i)
{f,c}
(ii)
{b,c,d,e}
(iii)
{a,b}
(iv)
{a,e,b}
(v)
{g,h,d}
Question
20
20.
Which of the following are true?
a)
cos
θ
=
1
cosec
θ
b)
cot
θ
=
1
sec
θ
c)
sec
θ
=
1
cos
θ
d)
tan
θ
=
1
cot
θ
e)
sec
θ
=
1
sin
θ
f)
cosec
θ
=
1
sin
θ
(i)
{b,d}
(ii)
{b,c,d}
(iii)
{a,c}
(iv)
{c,d,f}
(v)
{e,a,f}
Question
21
21.
Which of the following are true?
a)
tan
90°
=
1
b)
sin
45°
=
1
c)
cos
0°
=
1
d)
sin
0°
=
1
e)
cos
45°
=
1
f)
sin
90°
=
1
g)
tan
0°
=
1
h)
cos
90°
=
1
(i)
{b,f}
(ii)
{d,e,c}
(iii)
{a,c}
(iv)
{c,f}
(v)
{g,f,c}
Question
22
22.
Which of the following are true?
a)
cos
0°
=
0
b)
sin
0°
=
0
c)
sin
45°
=
0
d)
sin
90°
=
0
e)
tan
0°
=
0
f)
cos
90°
=
0
g)
cos
45°
=
0
h)
tan
90°
=
0
(i)
{c,e}
(ii)
{a,b}
(iii)
{b,e,f}
(iv)
{d,g,f}
(v)
{h,b,e}
Question
23
23.
Which of the following are true?
a)
cot
(
90
−
θ
)
=
tan
θ
b)
cosec
(
90
−
θ
)
=
sec
θ
c)
cos
(
90
−
θ
)
=
cos
θ
d)
sec
(
90
−
θ
)
=
cosec
θ
e)
tan
(
90
−
θ
)
=
−
tan
θ
f)
cos
(
90
−
θ
)
=
cot
θ
(i)
{e,b}
(ii)
{e,a,b}
(iii)
{a,b,d}
(iv)
{c,a}
(v)
{f,c,d}
Question
24
24.
Which of the following are true?
a)
tan
(
90
−
θ
)
=
cot
θ
b)
cot
(
90
−
θ
)
=
tan
θ
c)
sin
(
90
−
θ
)
=
−
sin
θ
d)
sin
(
90
−
θ
)
=
cos
θ
e)
cos
(
90
−
θ
)
=
−
cos
θ
f)
cos
(
90
−
θ
)
=
sin
θ
(i)
{c,a}
(ii)
{c,e,d}
(iii)
{a,b,d,f}
(iv)
{e,b}
(v)
{c,f,a}
Question
25
25.
If
q
=
cos
θ
+
sin
θ
,
r
=
cos
θ
sin
θ
then
(i)
q
2
=
(
2
r
+
1
)
(ii)
(
q
2
+
r
2
)
=
1
(iii)
(
q
2
−
r
2
)
=
1
(iv)
q
2
=
(
−
2
r
+
1
)
(v)
(
q
2
+
r
2
)
=
0
Question
26
26.
If
w
=
cos
θ
+
sin
θ
,
x
=
cos
θ
−
sin
θ
then
(i)
(
w
2
+
x
2
)
=
0
(ii)
(
w
2
−
x
2
)
=
2
(iii)
(
w
2
+
x
2
)
=
2
(iv)
(
w
2
−
x
2
)
=
1
(v)
(
w
2
+
x
2
)
=
1
Question
27
27.
If
f
=
v
cos
θ
+
w
sin
θ
and
g
=
v
sin
θ
−
w
cos
θ
, then
(i)
(
f
2
+
g
2
)
=
(
v
2
+
w
2
)
(ii)
f
g
=
v
w
(iii)
(
f
2
−
g
2
)
=
(
v
2
−
w
2
)
(iv)
(
v
2
+
f
2
)
=
(
w
2
+
g
2
)
Assignment Key
1) (iv)
2) (ii)
3) (i)
4) (iii)
5) (v)
6) (iv)
7) (v)
8) (iv)
9) (ii)
10) (iv)
11) (i)
12) (ii)
13) (i)
14) (v)
15) (iv)
16) (i)
17) (iv)
18) (ii)
19) (ii)
20) (iv)
21) (iv)
22) (iii)
23) (iii)
24) (iii)
25) (i)
26) (iii)
27) (i)
