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)
sec
2
θ
+
tan
2
θ
=
1
,
0 ≤ θ ≤ 90°
c)
sec
2
θ
−
tan
2
θ
=
1
,
0 ≤ θ ≤ 90°
d)
cosec
2
θ
+
cot
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)
{a,c,e}
(ii)
{f,b,e}
(iii)
{d,a,c}
(iv)
{b,a}
(v)
{d,c}
Question
2
2.
sin
2
60°
+
sin
2
30°
cos
2
20°
+
cos
2
70°
=
(i)
-1
(ii)
2
(iii)
1
(iv)
undefined
(v)
0
Question
3
3.
Which of the following are true?
a)
1
+
sin
θ
cos
θ
+
cos
θ
1
+
sin
θ
=
2
sec
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)
(
sec
θ
−
tan
θ
)
2
=
1
−
sin
θ
1
+
sin
θ
e)
(
sec
θ
−
tan
θ
)
2
=
1
+
sin
θ
1
−
sin
θ
(i)
{c,a,b}
(ii)
{c,a}
(iii)
{c,e,d}
(iv)
{a,b,d}
(v)
{e,b}
Question
4
4.
Which of the following are true?
a)
cos
3
θ
+
sin
3
θ
=
(
sin
θ
+
cos
θ
)
(
1
−
sin
θ
cos
θ
)
b)
sec
θ
1
+
cosec
θ
=
1
−
cosec
θ
sec
θ
c)
(
sin
θ
−
cos
θ
)
2
=
1
+
sin
2
θ
d)
cos
3
θ
−
sin
3
θ
=
(
sin
θ
+
cos
θ
)
(
1
−
sin
θ
cos
θ
)
e)
(
sin
θ
+
cos
θ
)
2
=
1
+
sin
2
θ
f)
(
sin
θ
+
cos
θ
)
2
+
(
sin
θ
−
cos
θ
)
2
=
2
g)
cos
θ
1
+
sin
θ
=
1
−
sin
θ
cos
θ
(i)
{b,a}
(ii)
{c,e}
(iii)
{d,b,f}
(iv)
{a,e,f,g}
(v)
{c,g,a}
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
−
t
2
)
=
1
(iv)
(
s
2
+
t
2
)
=
1
(v)
s
2
=
(
2
t
+
1
)
Question
6
6.
If
x
=
cos
θ
+
sin
θ
,
y
=
cos
θ
−
sin
θ
then
(i)
(
x
2
−
y
2
)
=
1
(ii)
(
x
2
+
y
2
)
=
1
(iii)
(
x
2
+
y
2
)
=
2
(iv)
(
x
2
−
y
2
)
=
2
(v)
(
x
2
+
y
2
)
=
0
Question
7
7.
a)
w
2
x
2
=
tan
2
θ
b)
(
w
2
+
x
2
)
=
d
2
c)
(
w
+
x
)
2
=
d
2
d)
2
w
x
=
d
2
sin
2
θ
e)
(
w
2
−
x
2
)
=
d
2
(i)
{c,a}
(ii)
{a,b,d}
(iii)
{e,b}
(iv)
{c,e,d}
(v)
{c,a,b}
Question
8
8.
If
e
=
w
cos
θ
+
x
sin
θ
and
f
=
w
sin
θ
−
x
cos
θ
, then
(i)
(
e
2
−
f
2
)
=
(
w
2
−
x
2
)
(ii)
e
f
=
w
x
(iii)
(
e
2
+
f
2
)
=
(
w
2
+
x
2
)
(iv)
(
w
2
+
e
2
)
=
(
x
2
+
f
2
)
Assignment Key
1) (i)
2) (iii)
3) (iv)
4) (iv)
5) (v)
6) (iii)
7) (ii)
8) (iii)
