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