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
tan
C
is always less than 1
c)
The value of
sin
C
is always less than 1
d)
The value of
cot
C
is always less than 1
e)
If
sin
C
= 0 , then
cos
C
= 1 or
cos
C
= -1
(i)
{b,e,c}
(ii)
{c,e}
(iii)
{a,c}
(iv)
{d,a,c}
(v)
{b,e}
Question
2
2.
For angle values from 0° to 90°, which of the following are true?
a)
The cosine value of the angle increases
b)
The product of the sine and cosine values remains a constant
c)
The tangent value of the angle increases
d)
The sine value of the angle increases
e)
The cotangent value of the angle increases
f)
The sum of the squares of the sine and cosine values remains a constant
(i)
{c,d,f}
(ii)
{a,c}
(iii)
{b,c,d}
(iv)
{e,a,f}
(v)
{b,d}
Question
3
3.
Which of the following are true?
a)
The cotangent of an angle is the reciprocal of the tangent of the angle.
b)
sin
(
G
+
H
)
=
sin
G
+
sin
H
c)
The cosine value of an angle is the reciprocal of the sine of the angle.
d)
The cosecant of an angle is the reciprocal of the secant of the angle
e)
cos
(
G
+
H
)
=
cos
G
+
cos
H
f)
tan
G
= tan
✕
G
(i)
{a}
(ii)
{b,a}
(iii)
{d,e,a}
(iv)
{f,a}
(v)
{c,a}
Question
4
4.
Which of the following are true?
a)
tan
θ
=
cot
θ
for no value of
θ
b)
sin
(
E
+
F
)
=
sin
E
+
sin
F
c)
The value of
sin
θ
increases as
θ
increases from
0°
to
90°
d)
cos
(
E
+
F
)
=
cos
E
+
cos
F
e)
tan
(
E
+
F
)
=
tan
E
+
tan
F
f)
The value of
cos
θ
increases as
θ
increases from
0°
to
90°
g)
sin
θ
=
cos
θ
for all
θ
(i)
{c}
(ii)
{f,c}
(iii)
{a,c}
(iv)
{b,c}
(v)
{d,e,c}
Question
5
5.
Which of the following are true?
a)
cos
2
A
=
cos
2
A
+
sin
2
A
b)
cos
2
A
=
cos
2
A
−
sin
2
A
c)
tan
2
A
=
2
tan
A
1
+
tan
2
A
d)
sin
2
A
=
2
sin
A
cos
A
e)
tan
2
A
=
2
tan
A
1
−
tan
2
A
f)
sin
2
A
=
2
sin
2
A
cos
2
A
(i)
{c,b,d}
(ii)
{f,a,e}
(iii)
{a,b}
(iv)
{c,d}
(v)
{b,d,e}
Question
6
6.
Which of the following are true?
a)
sin
42°
=
2
sin
21°
cos
21°
b)
cos
42°
=
cos
2
21°
−
sin
2
21°
c)
tan
42°
=
2
tan
21°
1
+
tan
2
21°
d)
sin
42°
=
2
sin
2
21°
cos
2
21°
e)
tan
42°
=
2
tan
21°
1
−
tan
2
21°
f)
cos
42°
=
cos
2
21°
+
sin
2
21°
(i)
{a,b,e}
(ii)
{d,b}
(iii)
{c,a}
(iv)
{f,c,e}
(v)
{d,a,b}
Question
7
7.
Which of the following are true?
a)
cos
θ
1
−
sin
θ
+
cos
θ
1
+
sin
θ
=
2
b)
cos
θ
cosec
θ
+
1
+
cos
θ
cosec
θ
−
1
=
2
tan
θ
c)
1
+
sin
θ
cos
θ
+
cos
θ
1
+
sin
θ
=
2
sec
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)
{a,b,c}
(ii)
{d,c}
(iii)
{a,b}
(iv)
{a,d,e}
(v)
{b,c,e}
Question
8
8.
Which of the following are true?
a)
(
sin
θ
+
cos
θ
)
2
+
(
sin
θ
−
cos
θ
)
2
=
2
b)
cos
3
θ
+
sin
3
θ
=
(
sin
θ
+
cos
θ
)
(
1
−
sin
θ
cos
θ
)
c)
cos
3
θ
−
sin
3
θ
=
(
sin
θ
+
cos
θ
)
(
1
−
sin
θ
cos
θ
)
d)
sec
θ
1
+
cosec
θ
=
1
−
cosec
θ
sec
θ
e)
(
sin
θ
−
cos
θ
)
2
=
1
+
sin
2
θ
f)
(
sin
θ
+
cos
θ
)
2
=
1
+
sin
2
θ
g)
cos
θ
1
+
sin
θ
=
1
−
sin
θ
cos
θ
(i)
{d,b}
(ii)
{c,a}
(iii)
{d,g,a}
(iv)
{a,b,f,g}
(v)
{e,c,f}
Question
9
9.
If
Q
,
R
and
S
are the interior angles of a triangle, then
sin
(
Q + R
2
)
=
(i)
sin
(
Q
2
)
(ii)
sin
(
S
2
)
(iii)
cos
(
S
2
)
(iv)
cos
(
Q
2
)
(v)
sin
S
Question
10
10.
Which of the following are true?
a)
sin
27°
=
cos
63°
b)
sin
36°
=
cos
36°
c)
tan
23°
=
cot
67°
d)
sec
50°
=
cosec
40°
e)
sin
34°
=
cos
56°
f)
cos
30°
=
sin
30°
g)
sin
21°
=
cos
69°
(i)
{b,f,d}
(ii)
{a,c,d,e,g}
(iii)
{f,c}
(iv)
{b,e,g}
(v)
{b,a}
Question
11
11.
Which of the following are true?
a)
sec
90°
is not defined
b)
tan
0°
is not defined
c)
cosec
0°
is not defined
d)
sec
0°
is not defined
e)
cot
90°
is not defined
f)
cot
0°
is not defined
g)
cosec
90°
is not defined
h)
tan
90°
is not defined
(i)
{a,c,f,h}
(ii)
{b,a}
(iii)
{d,c}
(iv)
{e,g,f}
(v)
{b,h,a}
Question
12
12.
Which of the following are true?
a)
cosec
θ
=
1
sin
θ
b)
cos
θ
=
1
cosec
θ
c)
tan
θ
=
1
cot
θ
d)
sec
θ
=
1
cos
θ
e)
cot
θ
=
1
sec
θ
f)
sec
θ
=
1
sin
θ
(i)
{b,a}
(ii)
{f,b,d}
(iii)
{a,c,d}
(iv)
{e,c}
(v)
{e,a,c}
Question
13
13.
Which of the following are true?
a)
sin
90°
=
1
b)
cos
0°
=
1
c)
tan
0°
=
1
d)
sin
45°
=
1
e)
sin
0°
=
1
f)
cos
90°
=
1
g)
tan
90°
=
1
h)
cos
45°
=
1
(i)
{g,b,a}
(ii)
{c,a}
(iii)
{d,b}
(iv)
{e,f,a}
(v)
{a,b}
Question
14
14.
Which of the following are true?
a)
tan
90°
=
0
b)
cos
90°
=
0
c)
cos
45°
=
0
d)
sin
45°
=
0
e)
cos
0°
=
0
f)
sin
90°
=
0
g)
sin
0°
=
0
h)
tan
0°
=
0
(i)
{d,e,h}
(ii)
{f,b,g}
(iii)
{a,b}
(iv)
{b,g,h}
(v)
{c,g}
Question
15
15.
If
r
=
cos
θ
+
sin
θ
,
s
=
cos
θ
sin
θ
then
(i)
r
2
=
(
2
s
+
1
)
(ii)
(
r
2
+
s
2
)
=
0
(iii)
(
r
2
−
s
2
)
=
1
(iv)
(
r
2
+
s
2
)
=
1
(v)
r
2
=
(
−
2
s
+
1
)
Question
16
16.
If
w
=
cos
θ
+
sin
θ
,
x
=
cos
θ
−
sin
θ
then
(i)
(
w
2
+
x
2
)
=
0
(ii)
(
w
2
+
x
2
)
=
1
(iii)
(
w
2
+
x
2
)
=
2
(iv)
(
w
2
−
x
2
)
=
1
(v)
(
w
2
−
x
2
)
=
2
Question
17
17.
a)
r
2
s
2
=
tan
2
θ
b)
(
r
2
+
s
2
)
=
c
2
c)
(
r
+
s
)
2
=
c
2
d)
2
r
s
=
c
2
sin
2
θ
e)
(
r
2
−
s
2
)
=
c
2
(i)
{c,e,d}
(ii)
{c,a,b}
(iii)
{a,b,d}
(iv)
{c,a}
(v)
{e,b}
Question
18
18.
If
f
=
y
cos
θ
+
z
sin
θ
and
g
=
y
sin
θ
−
z
cos
θ
, then
(i)
(
y
2
+
f
2
)
=
(
z
2
+
g
2
)
(ii)
(
f
2
−
g
2
)
=
(
y
2
−
z
2
)
(iii)
f
g
=
y
z
(iv)
(
f
2
+
g
2
)
=
(
y
2
+
z
2
)
Assignment Key
1) (ii)
2) (i)
3) (i)
4) (i)
5) (v)
6) (i)
7) (v)
8) (iv)
9) (iii)
10) (ii)
11) (i)
12) (iii)
13) (v)
14) (iv)
15) (i)
16) (iii)
17) (iii)
18) (iv)
