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