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)
The value of
cot
E
is always less than 1
b)
The value of
sin
E
is always less than 1
c)
The value of
tan
E
is always less than 1
d)
If
sin
E
= 0 , then
cos
E
= 1 or
cos
E
= -1
e)
cos
E
is the abbrieviation for
cosec
E
(i)
{b,d}
(ii)
{a,b}
(iii)
{e,a,b}
(iv)
{c,d}
(v)
{c,d,b}
Question
2
2.
For angle values from 0° to 90°, which of the following are true?
a)
The cotangent 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 sum of the squares of the sine and cosine values remains a constant
e)
The cosine value of the angle increases
f)
The sine value of the angle increases
(i)
{e,a,f}
(ii)
{c,d,f}
(iii)
{b,d}
(iv)
{b,c,d}
(v)
{a,c}
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
(
A
+
B
)
=
sin
A
+
sin
B
c)
tan
A
= tan
✕
A
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)
cos
(
A
+
B
)
=
cos
A
+
cos
B
(i)
{c,a}
(ii)
{a}
(iii)
{d,e,a}
(iv)
{b,a}
(v)
{f,a}
Question
4
4.
Which of the following are true?
a)
sin
(
A
+
B
)
=
sin
A
+
sin
B
b)
tan
(
A
+
B
)
=
tan
A
+
tan
B
c)
The value of
sin
θ
increases as
θ
increases from
0°
to
90°
d)
sin
θ
=
cos
θ
for all
θ
e)
tan
θ
=
cot
θ
for no value of
θ
f)
cos
(
A
+
B
)
=
cos
A
+
cos
B
g)
The value of
cos
θ
increases as
θ
increases from
0°
to
90°
(i)
{d,e,c}
(ii)
{a,c}
(iii)
{c}
(iv)
{b,c}
(v)
{f,c}
Question
5
5.
Which of the following are true?
a)
sin
2
A
=
2
sin
2
A
cos
2
A
b)
cos
2
A
=
cos
2
A
−
sin
2
A
c)
cos
2
A
=
cos
2
A
+
sin
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,d,f}
(ii)
{c,b,d}
(iii)
{c,d}
(iv)
{e,a,f}
(v)
{a,b}
Question
6
6.
Which of the following are true?
a)
cos
96°
=
cos
2
48°
+
sin
2
48°
b)
tan
96°
=
2
tan
48°
1
−
tan
2
48°
c)
cos
96°
=
cos
2
48°
−
sin
2
48°
d)
sin
96°
=
2
sin
48°
cos
48°
e)
sin
96°
=
2
sin
2
48°
cos
2
48°
f)
tan
96°
=
2
tan
48°
1
+
tan
2
48°
(i)
{e,b,c}
(ii)
{a,b}
(iii)
{e,c}
(iv)
{b,c,d}
(v)
{f,a,d}
Question
7
7.
Which of the following are true?
a)
1
+
sin
θ
cos
θ
+
cos
θ
1
+
sin
θ
=
2
sec
θ
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)
cos
θ
cosec
θ
+
1
+
cos
θ
cosec
θ
−
1
=
2
tan
θ
e)
cos
θ
1
−
sin
θ
+
cos
θ
1
+
sin
θ
=
2
(i)
{b,e,d}
(ii)
{b,a}
(iii)
{a,c,d}
(iv)
{b,a,c}
(v)
{e,c}
Question
8
8.
Which of the following are true?
a)
cos
3
θ
+
sin
3
θ
=
(
sin
θ
+
cos
θ
)
(
1
−
sin
θ
cos
θ
)
b)
cos
θ
1
+
sin
θ
=
1
−
sin
θ
cos
θ
c)
sec
θ
1
+
cosec
θ
=
1
−
cosec
θ
sec
θ
d)
(
sin
θ
+
cos
θ
)
2
=
1
+
sin
2
θ
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
+
(
sin
θ
−
cos
θ
)
2
=
2
(i)
{e,b}
(ii)
{e,g,a}
(iii)
{f,c,d}
(iv)
{a,b,d,g}
(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
S
(iii)
cos
(
S
2
)
(iv)
cos
(
Q
2
)
(v)
sin
(
Q
2
)
Question
10
10.
Which of the following are true?
a)
sin
24°
=
cos
24°
b)
tan
57°
=
cot
33°
c)
sin
35°
=
cos
55°
d)
sec
43°
=
cosec
47°
e)
sin
41°
=
cos
49°
f)
cos
38°
=
sin
38°
g)
sin
22°
=
cos
68°
(i)
{a,b}
(ii)
{a,e,g}
(iii)
{b,c,d,e,g}
(iv)
{f,c}
(v)
{a,f,d}
Question
11
11.
Which of the following are true?
a)
sec
0°
is not defined
b)
sec
90°
is not defined
c)
cosec
0°
is not defined
d)
cot
0°
is not defined
e)
cosec
90°
is not defined
f)
cot
90°
is not defined
g)
tan
90°
is not defined
h)
tan
0°
is not defined
(i)
{a,b}
(ii)
{a,g,b}
(iii)
{b,c,d,g}
(iv)
{e,c}
(v)
{f,h,d}
Question
12
12.
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)
sec
θ
=
1
sin
θ
e)
tan
θ
=
1
cot
θ
f)
cosec
θ
=
1
sin
θ
(i)
{b,c,e}
(ii)
{d,a,f}
(iii)
{b,e}
(iv)
{c,e,f}
(v)
{a,c}
Question
13
13.
Which of the following are true?
a)
sin
45°
=
1
b)
cos
90°
=
1
c)
sin
0°
=
1
d)
cos
0°
=
1
e)
tan
90°
=
1
f)
tan
0°
=
1
g)
cos
45°
=
1
h)
sin
90°
=
1
(i)
{f,h,d}
(ii)
{d,h}
(iii)
{b,h}
(iv)
{a,d}
(v)
{c,e,d}
Question
14
14.
Which of the following are true?
a)
tan
0°
=
0
b)
sin
0°
=
0
c)
tan
90°
=
0
d)
cos
45°
=
0
e)
sin
90°
=
0
f)
cos
90°
=
0
g)
cos
0°
=
0
h)
sin
45°
=
0
(i)
{e,g,f}
(ii)
{h,a,b}
(iii)
{d,b}
(iv)
{c,a}
(v)
{a,b,f}
Question
15
15.
If
w
=
cos
θ
+
sin
θ
,
x
=
cos
θ
sin
θ
then
(i)
(
w
2
−
x
2
)
=
1
(ii)
w
2
=
(
−
2
x
+
1
)
(iii)
(
w
2
+
x
2
)
=
0
(iv)
(
w
2
+
x
2
)
=
1
(v)
w
2
=
(
2
x
+
1
)
Question
16
16.
If
y
=
cos
θ
+
sin
θ
,
z
=
cos
θ
−
sin
θ
then
(i)
(
y
2
+
z
2
)
=
1
(ii)
(
y
2
−
z
2
)
=
1
(iii)
(
y
2
+
z
2
)
=
0
(iv)
(
y
2
+
z
2
)
=
2
(v)
(
y
2
−
z
2
)
=
2
Question
17
17.
a)
(
y
+
z
)
2
=
a
2
b)
2
y
z
=
a
2
sin
2
θ
c)
(
y
2
+
z
2
)
=
a
2
d)
y
2
z
2
=
tan
2
θ
e)
(
y
2
−
z
2
)
=
a
2
(i)
{a,b,c}
(ii)
{a,b}
(iii)
{a,e,d}
(iv)
{b,c,d}
(v)
{e,c}
Question
18
18.
If
d
=
u
cos
θ
+
v
sin
θ
and
e
=
u
sin
θ
−
v
cos
θ
, then
(i)
(
d
2
+
e
2
)
=
(
u
2
+
v
2
)
(ii)
(
u
2
+
d
2
)
=
(
v
2
+
e
2
)
(iii)
(
d
2
−
e
2
)
=
(
u
2
−
v
2
)
(iv)
d
e
=
u
v
Assignment Key
1) (i)
2) (ii)
3) (ii)
4) (iii)
5) (i)
6) (iv)
7) (iii)
8) (iv)
9) (iii)
10) (iii)
11) (iii)
12) (iv)
13) (ii)
14) (v)
15) (v)
16) (iv)
17) (iv)
18) (i)
