EduSahara™ Assignment
Name : Trigonometric Identities
Chapter : Trigonometrical Identities
Grade : ICSE 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)
sin
2
θ
−
cos
2
θ
=
1
,
0 ≤ θ ≤ 90°
f)
sec
2
θ
+
tan
2
θ
=
1
,
0 ≤ θ ≤ 90°
(i)
{a,b,d}
(ii)
{e,b}
(iii)
{c,a}
(iv)
{e,a,b}
(v)
{f,c,d}
Question
2
2.
1
+
tan
2
θ
1
+
cot
2
θ
=
(i)
tan
2
θ
(ii)
cosec
2
θ
(iii)
cot
2
θ
(iv)
1
(v)
sec
2
θ
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)
{d,b}
(ii)
{c,a}
(iii)
{c,a,b}
(iv)
{c,d,e}
(v)
{a,b,e}
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)
(
sin
θ
+
cos
θ
)
2
=
1
+
sin
2
θ
c)
cos
θ
1
+
sin
θ
=
1
−
sin
θ
cos
θ
d)
sec
θ
1
+
cosec
θ
=
1
−
cosec
θ
sec
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
3
θ
−
sin
3
θ
=
(
sin
θ
+
cos
θ
)
(
1
−
sin
θ
cos
θ
)
(i)
{e,b}
(ii)
{d,a}
(iii)
{g,d,c}
(iv)
{a,b,c,f}
(v)
{e,f,a}
Question
5
5.
If
v
=
cos
θ
+
sin
θ
,
w
=
cos
θ
sin
θ
then
(i)
v
2
=
(
−
2
w
+
1
)
(ii)
(
v
2
+
w
2
)
=
0
(iii)
(
v
2
+
w
2
)
=
1
(iv)
v
2
=
(
2
w
+
1
)
(v)
(
v
2
−
w
2
)
=
1
Question
6
6.
If
p
=
cos
θ
+
sin
θ
,
q
=
cos
θ
−
sin
θ
then
(i)
(
p
2
+
q
2
)
=
2
(ii)
(
p
2
−
q
2
)
=
2
(iii)
(
p
2
−
q
2
)
=
1
(iv)
(
p
2
+
q
2
)
=
1
(v)
(
p
2
+
q
2
)
=
0
Question
7
7.
a)
(
y
2
−
z
2
)
=
f
2
b)
(
y
+
z
)
2
=
f
2
c)
y
2
z
2
=
tan
2
θ
d)
(
y
2
+
z
2
)
=
f
2
e)
2
y
z
=
f
2
sin
2
θ
(i)
{c,d,e}
(ii)
{a,c,d}
(iii)
{a,c}
(iv)
{a,b,e}
(v)
{b,d}
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)
(
w
2
+
e
2
)
=
(
x
2
+
f
2
)
(iii)
(
e
2
+
f
2
)
=
(
w
2
+
x
2
)
(iv)
e
f
=
w
x
Assignment Key
1) (i)
2) (i)
3) (v)
4) (iv)
5) (iv)
6) (i)
7) (i)
8) (iii)
