EduSahara™ Assignment
Name : Trigonometric Identities
Chapter : Introduction to Trigonometry
Grade : CBSE Grade X
License : Non Commercial Use
Question
1
1.
Which of the following are true?
a)
cosec
2
θ
−
cot
2
θ
=
1
,
0 ≤ θ ≤ 90°
b)
sec
2
θ
+
tan
2
θ
=
1
,
0 ≤ θ ≤ 90°
c)
sin
2
θ
+
cos
2
θ
=
1
,
0 ≤ θ ≤ 90°
d)
sec
2
θ
−
tan
2
θ
=
1
,
0 ≤ θ ≤ 90°
e)
cosec
2
θ
+
cot
2
θ
=
1
,
0 ≤ θ ≤ 90°
f)
sin
2
θ
−
cos
2
θ
=
1
,
0 ≤ θ ≤ 90°
(i)
{e,a,c}
(ii)
{a,c,d}
(iii)
{e,c}
(iv)
{f,b,d}
(v)
{b,a}
Question
2
2.
sin
2
30°
+
sin
2
60°
cos
2
35°
+
cos
2
55°
=
(i)
1
(ii)
2
(iii)
-1
(iv)
undefined
(v)
0
Question
3
3.
Which of the following are true?
a)
(
sec
θ
−
tan
θ
)
2
=
1
+
sin
θ
1
−
sin
θ
b)
cos
θ
cosec
θ
+
1
+
cos
θ
cosec
θ
−
1
=
2
tan
θ
c)
cos
θ
1
−
sin
θ
+
cos
θ
1
+
sin
θ
=
2
d)
1
+
sin
θ
cos
θ
+
cos
θ
1
+
sin
θ
=
2
sec
θ
e)
(
sec
θ
−
tan
θ
)
2
=
1
−
sin
θ
1
+
sin
θ
(i)
{c,d}
(ii)
{a,b}
(iii)
{a,b,d}
(iv)
{a,c,e}
(v)
{b,d,e}
Question
4
4.
Which of the following are true?
a)
(
sin
θ
−
cos
θ
)
2
=
1
+
sin
2
θ
b)
cos
3
θ
−
sin
3
θ
=
(
sin
θ
+
cos
θ
)
(
1
−
sin
θ
cos
θ
)
c)
(
sin
θ
+
cos
θ
)
2
+
(
sin
θ
−
cos
θ
)
2
=
2
d)
cos
θ
1
+
sin
θ
=
1
−
sin
θ
cos
θ
e)
cos
3
θ
+
sin
3
θ
=
(
sin
θ
+
cos
θ
)
(
1
−
sin
θ
cos
θ
)
f)
sec
θ
1
+
cosec
θ
=
1
−
cosec
θ
sec
θ
g)
(
sin
θ
+
cos
θ
)
2
=
1
+
sin
2
θ
(i)
{f,a,e}
(ii)
{b,g,c}
(iii)
{a,c}
(iv)
{c,d,e,g}
(v)
{b,d}
Question
5
5.
If
s
=
cos
θ
+
sin
θ
,
t
=
cos
θ
sin
θ
then
(i)
(
s
2
+
t
2
)
=
0
(ii)
s
2
=
(
−
2
t
+
1
)
(iii)
s
2
=
(
2
t
+
1
)
(iv)
(
s
2
+
t
2
)
=
1
(v)
(
s
2
−
t
2
)
=
1
Question
6
6.
If
p
=
cos
θ
+
sin
θ
,
q
=
cos
θ
−
sin
θ
then
(i)
(
p
2
−
q
2
)
=
1
(ii)
(
p
2
−
q
2
)
=
2
(iii)
(
p
2
+
q
2
)
=
0
(iv)
(
p
2
+
q
2
)
=
2
(v)
(
p
2
+
q
2
)
=
1
Question
7
7.
a)
t
2
u
2
=
tan
2
θ
b)
(
t
2
−
u
2
)
=
f
2
c)
2
t
u
=
f
2
sin
2
θ
d)
(
t
2
+
u
2
)
=
f
2
e)
(
t
+
u
)
2
=
f
2
(i)
{b,a,c}
(ii)
{b,a}
(iii)
{a,c,d}
(iv)
{b,e,d}
(v)
{e,c}
Question
8
8.
If
f
=
q
cos
θ
+
r
sin
θ
and
g
=
q
sin
θ
−
r
cos
θ
, then
(i)
(
f
2
+
g
2
)
=
(
q
2
+
r
2
)
(ii)
f
g
=
q
r
(iii)
(
q
2
+
f
2
)
=
(
r
2
+
g
2
)
(iv)
(
f
2
−
g
2
)
=
(
q
2
−
r
2
)
Assignment Key
1) (ii)
2) (i)
3) (v)
4) (iv)
5) (iii)
6) (iv)
7) (iii)
8) (i)
