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