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
A
is the abbrieviation for
cosec
A
b)
The value of
cot
A
is always less than 1
c)
The value of
tan
A
is always less than 1
d)
If
sin
A
= 0 , then
cos
A
= 1 or
cos
A
= -1
e)
The value of
sin
A
is always less than 1
(i)
{a,d}
(ii)
{b,e,d}
(iii)
{d,e}
(iv)
{b,e}
(v)
{c,a,d}
Question
2
2.
For angle values from 0° to 90°, which of the following are true?
a)
The product of the sine and cosine values remains a constant
b)
The tangent value of the angle increases
c)
The cosine value of the angle increases
d)
The cotangent value of the angle increases
e)
The sine value of the angle increases
f)
The sum of the squares of the sine and cosine values remains a constant
(i)
{a,b}
(ii)
{c,b,e}
(iii)
{c,e}
(iv)
{b,e,f}
(v)
{d,a,f}
Question
3
3.
Which of the following are true?
a)
The cosecant of an angle is the reciprocal of the secant of the angle
b)
sin
(
E
+
F
)
=
sin
E
+
sin
F
c)
tan
E
= tan
✕
E
d)
The cosine value of an angle is the reciprocal of the sine of the angle.
e)
cos
(
E
+
F
)
=
cos
E
+
cos
F
f)
The cotangent of an angle is the reciprocal of the tangent of the angle.
(i)
{c,d,f}
(ii)
{b,f}
(iii)
{e,f}
(iv)
{f}
(v)
{a,f}
Question
4
4.
Which of the following are true?
a)
sin
(
F
+
G
)
=
sin
F
+
sin
G
b)
tan
(
F
+
G
)
=
tan
F
+
tan
G
c)
tan
θ
=
cot
θ
for no value of
θ
d)
The value of
cos
θ
increases as
θ
increases from
0°
to
90°
e)
cos
(
F
+
G
)
=
cos
F
+
cos
G
f)
The value of
sin
θ
increases as
θ
increases from
0°
to
90°
g)
sin
θ
=
cos
θ
for all
θ
(i)
{b,f}
(ii)
{c,d,f}
(iii)
{a,f}
(iv)
{f}
(v)
{e,f}
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)
sin
2
A
=
2
sin
2
A
cos
2
A
d)
tan
2
A
=
2
tan
A
1
+
tan
2
A
e)
tan
2
A
=
2
tan
A
1
−
tan
2
A
f)
sin
2
A
=
2
sin
A
cos
A
(i)
{b,e,f}
(ii)
{a,b}
(iii)
{d,a,f}
(iv)
{c,e}
(v)
{c,b,e}
Question
6
6.
Which of the following are true?
a)
cos
80°
=
cos
2
40°
−
sin
2
40°
b)
tan
80°
=
2
tan
40°
1
−
tan
2
40°
c)
cos
80°
=
cos
2
40°
+
sin
2
40°
d)
sin
80°
=
2
sin
2
40°
cos
2
40°
e)
tan
80°
=
2
tan
40°
1
+
tan
2
40°
f)
sin
80°
=
2
sin
40°
cos
40°
(i)
{d,b}
(ii)
{a,b,f}
(iii)
{c,a}
(iv)
{e,c,f}
(v)
{d,a,b}
Question
7
7.
Which of the following are true?
a)
(
sec
θ
−
tan
θ
)
2
=
1
−
sin
θ
1
+
sin
θ
b)
(
sec
θ
−
tan
θ
)
2
=
1
+
sin
θ
1
−
sin
θ
c)
cos
θ
cosec
θ
+
1
+
cos
θ
cosec
θ
−
1
=
2
tan
θ
d)
1
+
sin
θ
cos
θ
+
cos
θ
1
+
sin
θ
=
2
sec
θ
e)
cos
θ
1
−
sin
θ
+
cos
θ
1
+
sin
θ
=
2
(i)
{b,e,d}
(ii)
{b,a,c}
(iii)
{b,a}
(iv)
{e,c}
(v)
{a,c,d}
Question
8
8.
Which of the following are true?
a)
cos
θ
1
+
sin
θ
=
1
−
sin
θ
cos
θ
b)
(
sin
θ
+
cos
θ
)
2
+
(
sin
θ
−
cos
θ
)
2
=
2
c)
(
sin
θ
−
cos
θ
)
2
=
1
+
sin
2
θ
d)
(
sin
θ
+
cos
θ
)
2
=
1
+
sin
2
θ
e)
sec
θ
1
+
cosec
θ
=
1
−
cosec
θ
sec
θ
f)
cos
3
θ
+
sin
3
θ
=
(
sin
θ
+
cos
θ
)
(
1
−
sin
θ
cos
θ
)
g)
cos
3
θ
−
sin
3
θ
=
(
sin
θ
+
cos
θ
)
(
1
−
sin
θ
cos
θ
)
(i)
{e,b}
(ii)
{g,c,d}
(iii)
{e,f,a}
(iv)
{a,b,d,f}
(v)
{c,a}
Question
9
9.
If
Q
,
R
and
S
are the interior angles of a triangle, then
sin
(
Q + R
2
)
=
(i)
sin
(
S
2
)
(ii)
sin
(
Q
2
)
(iii)
cos
(
Q
2
)
(iv)
cos
(
S
2
)
(v)
sin
S
Question
10
10.
Which of the following are true?
a)
tan
34°
=
cot
56°
b)
cos
55°
=
sin
55°
c)
sin
35°
=
cos
55°
d)
sec
58°
=
cosec
32°
e)
sin
30°
=
cos
60°
f)
sin
41°
=
cos
41°
g)
sin
52°
=
cos
38°
(i)
{b,a}
(ii)
{a,c,d,e,g}
(iii)
{b,e,g}
(iv)
{f,c}
(v)
{b,f,d}
Question
11
11.
Which of the following are true?
a)
tan
90°
is not defined
b)
tan
0°
is not defined
c)
cosec
90°
is not defined
d)
sec
0°
is not defined
e)
sec
90°
is not defined
f)
cot
90°
is not defined
g)
cot
0°
is not defined
h)
cosec
0°
is not defined
(i)
{a,e,g,h}
(ii)
{b,h,a}
(iii)
{d,f,g}
(iv)
{c,e}
(v)
{b,a}
Question
12
12.
Which of the following are true?
a)
tan
θ
=
1
cot
θ
b)
sec
θ
=
1
cos
θ
c)
cot
θ
=
1
sec
θ
d)
cos
θ
=
1
cosec
θ
e)
cosec
θ
=
1
sin
θ
f)
sec
θ
=
1
sin
θ
(i)
{a,b,e}
(ii)
{f,c,e}
(iii)
{d,a,b}
(iv)
{d,b}
(v)
{c,a}
Question
13
13.
Which of the following are true?
a)
tan
90°
=
1
b)
sin
45°
=
1
c)
tan
0°
=
1
d)
cos
90°
=
1
e)
sin
0°
=
1
f)
cos
0°
=
1
g)
sin
90°
=
1
h)
cos
45°
=
1
(i)
{f,g}
(ii)
{a,f}
(iii)
{b,g}
(iv)
{e,g,f}
(v)
{c,d,f}
Question
14
14.
Which of the following are true?
a)
tan
0°
=
0
b)
sin
90°
=
0
c)
sin
45°
=
0
d)
cos
0°
=
0
e)
cos
45°
=
0
f)
tan
90°
=
0
g)
cos
90°
=
0
h)
sin
0°
=
0
(i)
{a,g,h}
(ii)
{f,a,g}
(iii)
{b,a}
(iv)
{c,g}
(v)
{d,e,h}
Question
15
15.
If
v
=
cos
θ
+
sin
θ
,
w
=
cos
θ
sin
θ
then
(i)
(
v
2
−
w
2
)
=
1
(ii)
v
2
=
(
−
2
w
+
1
)
(iii)
(
v
2
+
w
2
)
=
0
(iv)
(
v
2
+
w
2
)
=
1
(v)
v
2
=
(
2
w
+
1
)
Question
16
16.
If
r
=
cos
θ
+
sin
θ
,
s
=
cos
θ
−
sin
θ
then
(i)
(
r
2
+
s
2
)
=
0
(ii)
(
r
2
+
s
2
)
=
2
(iii)
(
r
2
−
s
2
)
=
2
(iv)
(
r
2
−
s
2
)
=
1
(v)
(
r
2
+
s
2
)
=
1
Question
17
17.
a)
(
u
2
+
v
2
)
=
e
2
b)
2
u
v
=
e
2
sin
2
θ
c)
(
u
+
v
)
2
=
e
2
d)
(
u
2
−
v
2
)
=
e
2
e)
u
2
v
2
=
tan
2
θ
(i)
{a,b,e}
(ii)
{c,a,b}
(iii)
{c,a}
(iv)
{c,d,e}
(v)
{d,b}
Question
18
18.
If
a
=
s
cos
θ
+
t
sin
θ
and
b
=
s
sin
θ
−
t
cos
θ
, then
(i)
(
s
2
+
a
2
)
=
(
t
2
+
b
2
)
(ii)
(
a
2
−
b
2
)
=
(
s
2
−
t
2
)
(iii)
(
a
2
+
b
2
)
=
(
s
2
+
t
2
)
(iv)
a
b
=
s
t
Assignment Key
1) (iii)
2) (iv)
3) (iv)
4) (iv)
5) (i)
6) (ii)
7) (v)
8) (iv)
9) (iv)
10) (ii)
11) (i)
12) (i)
13) (i)
14) (i)
15) (v)
16) (ii)
17) (i)
18) (iii)
