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)
cosec
2
θ
+
cot
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)
{d,c}
(ii)
{f,b,e}
(iii)
{a,c,e}
(iv)
{b,a}
(v)
{d,a,c}
Question
2
2.
sin
2
65°
+
sin
2
25°
cos
2
10°
+
cos
2
80°
=
(i)
1
(ii)
-1
(iii)
2
(iv)
undefined
(v)
0
Question
3
3.
Which of the following are true?
a)
cos
θ
cosec
θ
+
1
+
cos
θ
cosec
θ
−
1
=
2
tan
θ
b)
cos
θ
1
−
sin
θ
+
cos
θ
1
+
sin
θ
=
2
c)
1
+
sin
θ
cos
θ
+
cos
θ
1
+
sin
θ
=
2
sec
θ
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)
{e,c}
(ii)
{b,e,d}
(iii)
{a,c,d}
(iv)
{b,a,c}
(v)
{b,a}
Question
4
4.
Which of the following are true?
a)
cos
θ
1
+
sin
θ
=
1
−
sin
θ
cos
θ
b)
cos
3
θ
−
sin
3
θ
=
(
sin
θ
+
cos
θ
)
(
1
−
sin
θ
cos
θ
)
c)
(
sin
θ
−
cos
θ
)
2
=
1
+
sin
2
θ
d)
(
sin
θ
+
cos
θ
)
2
=
1
+
sin
2
θ
e)
sec
θ
1
+
cosec
θ
=
1
−
cosec
θ
sec
θ
f)
(
sin
θ
+
cos
θ
)
2
+
(
sin
θ
−
cos
θ
)
2
=
2
g)
cos
3
θ
+
sin
3
θ
=
(
sin
θ
+
cos
θ
)
(
1
−
sin
θ
cos
θ
)
(i)
{b,a}
(ii)
{a,d,f,g}
(iii)
{c,g,a}
(iv)
{c,d}
(v)
{e,b,f}
Question
5
5.
If
w
=
cos
θ
+
sin
θ
,
x
=
cos
θ
sin
θ
then
(i)
w
2
=
(
−
2
x
+
1
)
(ii)
(
w
2
+
x
2
)
=
1
(iii)
(
w
2
−
x
2
)
=
1
(iv)
(
w
2
+
x
2
)
=
0
(v)
w
2
=
(
2
x
+
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
)
=
2
(iii)
(
y
2
+
z
2
)
=
1
(iv)
(
y
2
−
z
2
)
=
2
(v)
(
y
2
+
z
2
)
=
0
Question
7
7.
a)
2
x
y
=
h
2
sin
2
θ
b)
(
x
2
+
y
2
)
=
h
2
c)
x
2
y
2
=
tan
2
θ
d)
(
x
+
y
)
2
=
h
2
e)
(
x
2
−
y
2
)
=
h
2
(i)
{e,b}
(ii)
{d,e,c}
(iii)
{a,b,c}
(iv)
{d,a}
(v)
{d,a,b}
Question
8
8.
If
c
=
w
cos
θ
+
x
sin
θ
and
d
=
w
sin
θ
−
x
cos
θ
, then
(i)
(
w
2
+
c
2
)
=
(
x
2
+
d
2
)
(ii)
c
d
=
w
x
(iii)
(
c
2
+
d
2
)
=
(
w
2
+
x
2
)
(iv)
(
c
2
−
d
2
)
=
(
w
2
−
x
2
)
Assignment Key
1) (iii)
2) (i)
3) (iii)
4) (ii)
5) (v)
6) (ii)
7) (iii)
8) (iii)
