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Byju's Answer
Standard XII
Mathematics
Trigonometric Equations
Find sinx2 ...
Question
Find
sin
x
2
,
cos
x
2
a
n
d
tan
x
2
in the following equation
tan
x
=
−
4
3
,
x
in quadrant II
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Solution
Give x is in quadrant II
So,
90
o
<
x
<
180
o
dividing with 2 all sides
95
<
x
<
90
So,
x
2
lies in
1
s
t
quadrant
i.e.,
sin
,
cos
&
tan
are positive
Given
tan
x
=
−
4
3
tan
x
=
2
tan
x
2
1
−
tan
2
x
2
=
−
4
3
−
4
(
1
−
t
a
n
2
x
2
)
=
6
tan
x
2
−
4
+
4
tan
2
x
2
=
6
tan
x
2
let
tan
x
2
=
a
4
a
2
−
6
a
−
4
=
0
4
a
−
8
a
+
2
a
−
4
=
0
(
4
a
+
2
)
(
a
−
2
)
=
0
So,
a
=
−
1
2
or
a
=
2
tan
x
2
=
−
1
2
or
tan
x
2
=
2
Since
x
2
is in first quadrant
tan
x
2
should be positive
∴
tan
x
2
=
2
cos
x
2
=
1
√
2
2
+
1
=
1
√
5
sin
x
2
=
2
√
2
2
+
1
=
2
√
5
cos
x
2
=
1
√
5
tan
x
2
=
2
sin
x
2
=
2
√
5
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0
Similar questions
Q.
Find
sin
x
2
,
cos
x
2
a
n
d
tan
x
2
in each of the following:
1:-
tan
x
=
−
4
3
,
x in quadrant
I
I
2:-
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−
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, x in quadrant
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