EduSahara™ Assignment
Name : Complex Trigonometric Expressions Simplification
Chapter : Trigonometry
Grade : SSC Grade X
License : Non Commercial Use
Question
1
1.
1
−
tan
2
θ
1
+
tan
2
θ
=
(i)
cos
2
θ
(ii)
tan
2
θ
(iii)
sin
2
θ
(iv)
cot
2
θ
Question
2
2.
1
−
tan
2
30°
1
+
tan
2
30°
=
(i)
cos
60°
(ii)
sin
60°
(iii)
tan
60°
(iv)
cot
60°
Question
3
3.
sin
2
65°
+
sin
2
25°
cos
2
40°
+
cos
2
50°
=
(i)
0
(ii)
undefined
(iii)
-1
(iv)
1
(v)
2
Question
4
4.
1
+
tan
2
θ
1
+
cot
2
θ
=
(i)
sec
2
θ
(ii)
cosec
2
θ
(iii)
1
(iv)
tan
2
θ
(v)
cot
2
θ
Question
5
5.
If
cot
θ
=
1
2
, find
(
1
+
sin
θ
)
(
1
−
sin
θ
)
(
1
−
cos
θ
)
(
1
+
cos
θ
)
(i)
(
-1
4
)
(ii)
1
2
(iii)
1
4
(iv)
1
6
(v)
3
4
Question
6
6.
If
tan
θ
=
3
7
, find
(
1
+
cos
θ
)
(
1
−
cos
θ
)
(
1
+
sin
θ
)
(
1
−
sin
θ
)
(i)
3
17
(ii)
9
47
(iii)
9
49
(iv)
1
7
(v)
11
49
Question
7
7.
Find the value of
(
1
+
sin
θ
)
(
cos
θ
)
+
(
cos
θ
)
(
1
+
sin
θ
)
(i)
2
cos
θ
(ii)
2
sec
θ
(iii)
2
cosec
θ
(iv)
2
sin
θ
Question
8
8.
Find the value of
9
sec
2
θ
−
9
tan
2
θ
(i)
9
(ii)
1
(iii)
11
(iv)
0
(v)
7
Question
9
9.
Find the value of
(
1
+
tan
θ
+
sec
θ
)
(
1
+
cot
θ
−
cosec
θ
)
(i)
5
(ii)
(-1)
(iii)
1
(iv)
2
(v)
3
Question
10
10.
Find the value of
(
cosec
θ
−
cot
θ
)
2
(i)
1
−
sin
θ
1
+
sin
θ
(ii)
1
+
sin
θ
1
−
sin
θ
(iii)
1
+
cos
θ
1
−
cos
θ
(iv)
1
−
cos
θ
1
+
cos
θ
Question
11
11.
If
tan
θ
+
cot
θ
=
6
, find
tan
2
θ
+
cot
2
θ
(i)
35
(ii)
31
(iii)
34
(iv)
33
(v)
37
Question
12
12.
If
tan
θ
−
cot
θ
=
8
, find
tan
2
θ
+
cot
2
θ
(i)
67
(ii)
65
(iii)
66
(iv)
63
(v)
69
Question
13
13.
Which of the following are true?
a)
(
sec
θ
−
tan
θ
)
2
=
1
−
sin
θ
1
+
sin
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)
cos
θ
cosec
θ
+
1
+
cos
θ
cosec
θ
−
1
=
2
tan
θ
e)
1
+
sin
θ
cos
θ
+
cos
θ
1
+
sin
θ
=
2
sec
θ
(i)
{b,c,e}
(ii)
{a,d,e}
(iii)
{b,a}
(iv)
{b,a,d}
(v)
{c,d}
Question
14
14.
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)
(
sin
θ
−
cos
θ
)
2
=
1
+
sin
2
θ
d)
(
sin
θ
+
cos
θ
)
2
+
(
sin
θ
−
cos
θ
)
2
=
2
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
θ
1
+
sin
θ
=
1
−
sin
θ
cos
θ
(i)
{a,b}
(ii)
{b,d,f,g}
(iii)
{c,d}
(iv)
{e,a,f}
(v)
{c,g,b}
Question
15
15.
If
T
,
U
and
V
are the interior angles of a triangle, then
sin
(
T + U
2
)
=
(i)
sin
(
V
2
)
(ii)
sin
(
T
2
)
(iii)
cos
(
V
2
)
(iv)
sin
V
(v)
cos
(
T
2
)
Question
16
16.
If
r
=
cos
θ
+
sin
θ
,
s
=
cos
θ
sin
θ
then
(i)
r
2
=
(
−
2
s
+
1
)
(ii)
r
2
=
(
2
s
+
1
)
(iii)
(
r
2
+
s
2
)
=
1
(iv)
(
r
2
−
s
2
)
=
1
(v)
(
r
2
+
s
2
)
=
0
Question
17
17.
If
q
=
cos
θ
+
sin
θ
,
r
=
cos
θ
−
sin
θ
then
(i)
(
q
2
+
r
2
)
=
0
(ii)
(
q
2
−
r
2
)
=
1
(iii)
(
q
2
+
r
2
)
=
1
(iv)
(
q
2
−
r
2
)
=
2
(v)
(
q
2
+
r
2
)
=
2
Question
18
18.
If
f
=
q
cos
θ
+
r
sin
θ
and
g
=
q
sin
θ
−
r
cos
θ
, then
(i)
(
q
2
+
f
2
)
=
(
r
2
+
g
2
)
(ii)
(
f
2
−
g
2
)
=
(
q
2
−
r
2
)
(iii)
f
g
=
q
r
(iv)
(
f
2
+
g
2
)
=
(
q
2
+
r
2
)
Assignment Key
1) (i)
2) (i)
3) (iv)
4) (iv)
5) (iii)
6) (iii)
7) (ii)
8) (i)
9) (iv)
10) (iv)
11) (iii)
12) (iii)
13) (ii)
14) (ii)
15) (iii)
16) (ii)
17) (v)
18) (iv)
