EduSahara™ Assignment
Name : Trigonometry Miscellaneous
Chapter : Introduction to Trigonometry
Grade : CBSE Grade X
License : Non Commercial Use
Question
1
1.
Which of the following are true?
a)
cos
C
is the abbrieviation for
cosec
C
b)
The value of
cot
C
is always less than 1
c)
The value of
tan
C
is always less than 1
d)
The value of
sin
C
is always less than 1
e)
If
sin
C
= 0 , then
cos
C
= 1 or
cos
C
= -1
(i)
{b,e}
(ii)
{c,a,d}
(iii)
{b,e,d}
(iv)
{a,d}
(v)
{d,e}
Question
2
2.
For angle values from 0° to 90°, which of the following are true?
a)
The sine value of the angle increases
b)
The tangent value of the angle increases
c)
The cotangent value of the angle increases
d)
The sum of the squares of the sine and cosine values remains a constant
e)
The product of the sine and cosine values remains a constant
f)
The cosine value of the angle increases
(i)
{c,a}
(ii)
{a,b,d}
(iii)
{e,b}
(iv)
{e,a,b}
(v)
{f,c,d}
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)
sin
(
F
+
G
)
=
sin
F
+
sin
G
c)
The cosecant of an angle is the reciprocal of the secant of the angle
d)
cos
(
F
+
G
)
=
cos
F
+
cos
G
e)
The cotangent of an angle is the reciprocal of the tangent of the angle.
f)
tan
F
= tan
✕
F
(i)
{e}
(ii)
{c,d,e}
(iii)
{a,e}
(iv)
{f,e}
(v)
{b,e}
Question
4
4.
Which of the following are true?
a)
The value of
cos
θ
increases as
θ
increases from
0°
to
90°
b)
The value of
sin
θ
increases as
θ
increases from
0°
to
90°
c)
sin
(
B
+
C
)
=
sin
B
+
sin
C
d)
tan
(
B
+
C
)
=
tan
B
+
tan
C
e)
tan
θ
=
cot
θ
for no value of
θ
f)
cos
(
B
+
C
)
=
cos
B
+
cos
C
g)
sin
θ
=
cos
θ
for all
θ
(i)
{d,e,b}
(ii)
{f,b}
(iii)
{b}
(iv)
{a,b}
(v)
{c,b}
Question
5
5.
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)
cos
2
A
=
cos
2
A
−
sin
2
A
f)
tan
2
A
=
2
tan
A
1
−
tan
2
A
(i)
{c,e}
(ii)
{d,b,f}
(iii)
{b,a}
(iv)
{c,a,e}
(v)
{a,e,f}
Question
6
6.
Which of the following are true?
a)
sin
60°
=
2
sin
30°
cos
30°
b)
cos
60°
=
cos
2
30°
+
sin
2
30°
c)
tan
60°
=
2
tan
30°
1
−
tan
2
30°
d)
tan
60°
=
2
tan
30°
1
+
tan
2
30°
e)
sin
60°
=
2
sin
2
30°
cos
2
30°
f)
cos
60°
=
cos
2
30°
−
sin
2
30°
(i)
{e,b,f}
(ii)
{d,a,c}
(iii)
{a,c,f}
(iv)
{d,c}
(v)
{b,a}
Question
7
7.
Which of the following are true?
a)
cos
θ
1
−
sin
θ
+
cos
θ
1
+
sin
θ
=
2
b)
1
+
sin
θ
cos
θ
+
cos
θ
1
+
sin
θ
=
2
sec
θ
c)
cos
θ
cosec
θ
+
1
+
cos
θ
cosec
θ
−
1
=
2
tan
θ
d)
(
sec
θ
−
tan
θ
)
2
=
1
−
sin
θ
1
+
sin
θ
e)
(
sec
θ
−
tan
θ
)
2
=
1
+
sin
θ
1
−
sin
θ
(i)
{b,c,d}
(ii)
{e,c}
(iii)
{a,e,d}
(iv)
{a,b,c}
(v)
{a,b}
Question
8
8.
Which of the following are true?
a)
sec
θ
1
+
cosec
θ
=
1
−
cosec
θ
sec
θ
b)
cos
θ
1
+
sin
θ
=
1
−
sin
θ
cos
θ
c)
(
sin
θ
+
cos
θ
)
2
+
(
sin
θ
−
cos
θ
)
2
=
2
d)
cos
3
θ
−
sin
3
θ
=
(
sin
θ
+
cos
θ
)
(
1
−
sin
θ
cos
θ
)
e)
(
sin
θ
−
cos
θ
)
2
=
1
+
sin
2
θ
f)
(
sin
θ
+
cos
θ
)
2
=
1
+
sin
2
θ
g)
cos
3
θ
+
sin
3
θ
=
(
sin
θ
+
cos
θ
)
(
1
−
sin
θ
cos
θ
)
(i)
{a,b}
(ii)
{b,c,f,g}
(iii)
{d,c}
(iv)
{d,g,b}
(v)
{e,a,f}
Question
9
9.
If
U
,
V
and
W
are the interior angles of a triangle, then
sin
(
U + V
2
)
=
(i)
sin
W
(ii)
sin
(
U
2
)
(iii)
sin
(
W
2
)
(iv)
cos
(
U
2
)
(v)
cos
(
W
2
)
Question
10
10.
Which of the following are true?
a)
tan
44°
=
cot
46°
b)
sin
43°
=
cos
47°
c)
sec
31°
=
cosec
59°
d)
sin
55°
=
cos
35°
e)
cos
23°
=
sin
23°
f)
sin
34°
=
cos
34°
g)
sin
32°
=
cos
58°
(i)
{e,d,g}
(ii)
{e,f,c}
(iii)
{f,b}
(iv)
{e,a}
(v)
{a,b,c,d,g}
Question
11
11.
Which of the following are true?
a)
cot
0°
is not defined
b)
cosec
90°
is not defined
c)
cosec
0°
is not defined
d)
sec
0°
is not defined
e)
tan
0°
is not defined
f)
tan
90°
is not defined
g)
sec
90°
is not defined
h)
cot
90°
is not defined
(i)
{b,g,a}
(ii)
{e,h,f}
(iii)
{d,c}
(iv)
{a,c,f,g}
(v)
{b,a}
Question
12
12.
Which of the following are true?
a)
tan
θ
=
1
cot
θ
b)
cos
θ
=
1
cosec
θ
c)
cosec
θ
=
1
sin
θ
d)
sec
θ
=
1
cos
θ
e)
sec
θ
=
1
sin
θ
f)
cot
θ
=
1
sec
θ
(i)
{e,a,c}
(ii)
{e,c}
(iii)
{f,b,d}
(iv)
{a,c,d}
(v)
{b,a}
Question
13
13.
Which of the following are true?
a)
cos
90°
=
1
b)
cos
0°
=
1
c)
sin
0°
=
1
d)
tan
90°
=
1
e)
cos
45°
=
1
f)
tan
0°
=
1
g)
sin
90°
=
1
h)
sin
45°
=
1
(i)
{d,e,b}
(ii)
{a,b}
(iii)
{f,g,b}
(iv)
{c,g}
(v)
{b,g}
Question
14
14.
Which of the following are true?
a)
cos
90°
=
0
b)
tan
0°
=
0
c)
sin
90°
=
0
d)
cos
45°
=
0
e)
tan
90°
=
0
f)
cos
0°
=
0
g)
sin
45°
=
0
h)
sin
0°
=
0
(i)
{a,b,h}
(ii)
{c,a}
(iii)
{g,a,b}
(iv)
{d,b}
(v)
{e,f,h}
Question
15
15.
If
u
=
cos
θ
+
sin
θ
,
v
=
cos
θ
sin
θ
then
(i)
u
2
=
(
−
2
v
+
1
)
(ii)
u
2
=
(
2
v
+
1
)
(iii)
(
u
2
+
v
2
)
=
0
(iv)
(
u
2
+
v
2
)
=
1
(v)
(
u
2
−
v
2
)
=
1
Question
16
16.
If
w
=
cos
θ
+
sin
θ
,
x
=
cos
θ
−
sin
θ
then
(i)
(
w
2
+
x
2
)
=
2
(ii)
(
w
2
−
x
2
)
=
2
(iii)
(
w
2
−
x
2
)
=
1
(iv)
(
w
2
+
x
2
)
=
1
(v)
(
w
2
+
x
2
)
=
0
Question
17
17.
a)
p
2
q
2
=
tan
2
θ
b)
(
p
2
+
q
2
)
=
a
2
c)
2
p
q
=
a
2
sin
2
θ
d)
(
p
+
q
)
2
=
a
2
e)
(
p
2
−
q
2
)
=
a
2
(i)
{d,e,c}
(ii)
{e,b}
(iii)
{d,a}
(iv)
{d,a,b}
(v)
{a,b,c}
Question
18
18.
If
c
=
x
cos
θ
+
y
sin
θ
and
d
=
x
sin
θ
−
y
cos
θ
, then
(i)
(
x
2
+
c
2
)
=
(
y
2
+
d
2
)
(ii)
(
c
2
−
d
2
)
=
(
x
2
−
y
2
)
(iii)
(
c
2
+
d
2
)
=
(
x
2
+
y
2
)
(iv)
c
d
=
x
y
Assignment Key
1) (v)
2) (ii)
3) (i)
4) (iii)
5) (v)
6) (iii)
7) (i)
8) (ii)
9) (v)
10) (v)
11) (iv)
12) (iv)
13) (v)
14) (i)
15) (ii)
16) (i)
17) (v)
18) (iii)
