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)
cosec
2
θ
−
cot
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)
sin
2
θ
+
cos
2
θ
=
1
,
0 ≤ θ ≤ 90°
(i)
{b,d}
(ii)
{c,d,f}
(iii)
{b,c,d}
(iv)
{a,c}
(v)
{e,a,f}
Question
2
2.
sin
2
15°
+
sin
2
75°
cos
2
30°
+
cos
2
60°
=
(i)
undefined
(ii)
-1
(iii)
0
(iv)
2
(v)
1
Question
3
3.
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)
cos
θ
1
−
sin
θ
+
cos
θ
1
+
sin
θ
=
2
d)
(
sec
θ
−
tan
θ
)
2
=
1
+
sin
θ
1
−
sin
θ
e)
cos
θ
cosec
θ
+
1
+
cos
θ
cosec
θ
−
1
=
2
tan
θ
(i)
{c,a}
(ii)
{c,d,e}
(iii)
{d,b}
(iv)
{c,a,b}
(v)
{a,b,e}
Question
4
4.
Which of the following are true?
a)
cos
θ
1
+
sin
θ
=
1
−
sin
θ
cos
θ
b)
sec
θ
1
+
cosec
θ
=
1
−
cosec
θ
sec
θ
c)
cos
3
θ
+
sin
3
θ
=
(
sin
θ
+
cos
θ
)
(
1
−
sin
θ
cos
θ
)
d)
(
sin
θ
+
cos
θ
)
2
+
(
sin
θ
−
cos
θ
)
2
=
2
e)
cos
3
θ
−
sin
3
θ
=
(
sin
θ
+
cos
θ
)
(
1
−
sin
θ
cos
θ
)
f)
(
sin
θ
+
cos
θ
)
2
=
1
+
sin
2
θ
g)
(
sin
θ
−
cos
θ
)
2
=
1
+
sin
2
θ
(i)
{e,c}
(ii)
{b,a}
(iii)
{a,c,d,f}
(iv)
{g,b,d}
(v)
{e,f,a}
Question
5
5.
If
y
=
cos
θ
+
sin
θ
,
z
=
cos
θ
sin
θ
then
(i)
y
2
=
(
2
z
+
1
)
(ii)
(
y
2
+
z
2
)
=
0
(iii)
(
y
2
+
z
2
)
=
1
(iv)
(
y
2
−
z
2
)
=
1
(v)
y
2
=
(
−
2
z
+
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
)
=
2
(iv)
(
p
2
+
q
2
)
=
0
(v)
(
p
2
+
q
2
)
=
1
Question
7
7.
a)
(
u
2
−
v
2
)
=
h
2
b)
(
u
+
v
)
2
=
h
2
c)
2
u
v
=
h
2
sin
2
θ
d)
(
u
2
+
v
2
)
=
h
2
e)
u
2
v
2
=
tan
2
θ
(i)
{a,c,d}
(ii)
{a,b,e}
(iii)
{c,d,e}
(iv)
{b,d}
(v)
{a,c}
Question
8
8.
If
c
=
y
cos
θ
+
z
sin
θ
and
d
=
y
sin
θ
−
z
cos
θ
, then
(i)
(
y
2
+
c
2
)
=
(
z
2
+
d
2
)
(ii)
(
c
2
+
d
2
)
=
(
y
2
+
z
2
)
(iii)
(
c
2
−
d
2
)
=
(
y
2
−
z
2
)
(iv)
c
d
=
y
z
Assignment Key
1) (ii)
2) (v)
3) (v)
4) (iii)
5) (i)
6) (iii)
7) (iii)
8) (ii)
