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)
sin
2
θ
−
cos
2
θ
=
1
,
0 ≤ θ ≤ 90°
b)
cosec
2
θ
+
cot
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)
sec
2
θ
−
tan
2
θ
=
1
,
0 ≤ θ ≤ 90°
f)
cosec
2
θ
−
cot
2
θ
=
1
,
0 ≤ θ ≤ 90°
(i)
{b,c,e}
(ii)
{b,e}
(iii)
{c,e,f}
(iv)
{d,a,f}
(v)
{a,c}
Question
2
2.
sin
2
75°
+
sin
2
15°
cos
2
25°
+
cos
2
65°
=
(i)
2
(ii)
-1
(iii)
undefined
(iv)
1
(v)
0
Question
3
3.
Which of the following are true?
a)
(
sec
θ
−
tan
θ
)
2
=
1
+
sin
θ
1
−
sin
θ
b)
1
+
sin
θ
cos
θ
+
cos
θ
1
+
sin
θ
=
2
sec
θ
c)
cos
θ
1
−
sin
θ
+
cos
θ
1
+
sin
θ
=
2
d)
cos
θ
cosec
θ
+
1
+
cos
θ
cosec
θ
−
1
=
2
tan
θ
e)
(
sec
θ
−
tan
θ
)
2
=
1
−
sin
θ
1
+
sin
θ
(i)
{b,d,e}
(ii)
{a,b,d}
(iii)
{a,b}
(iv)
{a,c,e}
(v)
{c,d}
Question
4
4.
Which of the following are true?
a)
(
sin
θ
+
cos
θ
)
2
=
1
+
sin
2
θ
b)
(
sin
θ
+
cos
θ
)
2
+
(
sin
θ
−
cos
θ
)
2
=
2
c)
sec
θ
1
+
cosec
θ
=
1
−
cosec
θ
sec
θ
d)
(
sin
θ
−
cos
θ
)
2
=
1
+
sin
2
θ
e)
cos
3
θ
+
sin
3
θ
=
(
sin
θ
+
cos
θ
)
(
1
−
sin
θ
cos
θ
)
f)
cos
θ
1
+
sin
θ
=
1
−
sin
θ
cos
θ
g)
cos
3
θ
−
sin
3
θ
=
(
sin
θ
+
cos
θ
)
(
1
−
sin
θ
cos
θ
)
(i)
{c,a}
(ii)
{d,b}
(iii)
{d,f,a}
(iv)
{a,b,e,f}
(v)
{g,c,e}
Question
5
5.
If
y
=
cos
θ
+
sin
θ
,
z
=
cos
θ
sin
θ
then
(i)
(
y
2
−
z
2
)
=
1
(ii)
(
y
2
+
z
2
)
=
0
(iii)
y
2
=
(
−
2
z
+
1
)
(iv)
(
y
2
+
z
2
)
=
1
(v)
y
2
=
(
2
z
+
1
)
Question
6
6.
If
s
=
cos
θ
+
sin
θ
,
t
=
cos
θ
−
sin
θ
then
(i)
(
s
2
+
t
2
)
=
1
(ii)
(
s
2
+
t
2
)
=
0
(iii)
(
s
2
−
t
2
)
=
1
(iv)
(
s
2
−
t
2
)
=
2
(v)
(
s
2
+
t
2
)
=
2
Question
7
7.
a)
(
v
2
+
w
2
)
=
d
2
b)
(
v
+
w
)
2
=
d
2
c)
v
2
w
2
=
tan
2
θ
d)
(
v
2
−
w
2
)
=
d
2
e)
2
v
w
=
d
2
sin
2
θ
(i)
{d,c}
(ii)
{a,c,e}
(iii)
{b,a}
(iv)
{b,a,c}
(v)
{b,d,e}
Question
8
8.
If
d
=
y
cos
θ
+
z
sin
θ
and
e
=
y
sin
θ
−
z
cos
θ
, then
(i)
(
y
2
+
d
2
)
=
(
z
2
+
e
2
)
(ii)
d
e
=
y
z
(iii)
(
d
2
+
e
2
)
=
(
y
2
+
z
2
)
(iv)
(
d
2
−
e
2
)
=
(
y
2
−
z
2
)
Assignment Key
1) (iii)
2) (iv)
3) (i)
4) (iv)
5) (v)
6) (v)
7) (ii)
8) (iii)
