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