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Byju's Answer
Standard XII
Mathematics
Equations Involving sinx + cosx and sinx.cosx
The number of...
Question
The number of solution of equation
2
sin
2
x
+
sin
x
(
1
−
2
cos
2
x
)
−
4
=
0
in the interval
(
0
,
π
) is -
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Solution
4
sin
x
cos
x
+
sin
x
(
1
−
2
(
2
cos
2
x
−
1
)
)
=
4
4
cos
x
+
1
−
4
cos
2
x
+
2
=
4
sin
x
4
−
(
2
cos
x
−
1
)
2
=
4
sin
x
⇒
L.H.S
≤
4
and
⇒
R.H.S
≥
4
and equality holds when
cos
x
=
1
2
and
sin
x
=
1
which is not possible.
Hence, no solution.
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