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