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Mathematics
The general solution of the equation sin 2x + 2 sin x +2 cos x + 1 = 0 is
Q. The general solution of the equation
sin
2
x
+
2
sin
x
+
2
cos
x
+
1
=
0
is
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BITSAT
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A
3
nπ
−
4
π
0%
B
2
nπ
+
4
π
33%
C
2
nπ
+
(
−
1
)
n
sin
−
1
(
3
1
)
33%
D
nπ
−
4
π
33%
Solution:
Given,
sin
2
x
+
2
sin
x
+
2
cos
x
+
1
=
0
⇒
1
+
sin
2
x
+
2
(
sin
x
+
cos
x
)
=
0
⇒
(
sin
x
+
cos
x
)
2
+
2
(
sin
x
+
cos
x
)
=
0
⇒
(
sin
x
+
cos
x
)
(
sin
x
+
cos
x
+
2
)
=
0
sin
x
+
cos
x
=
0
or
sin
x
+
cos
x
=
−
2
But,
sin
x
+
cos
x
=
−
2
is inadmissible.
Since,
∣
sin
x
∣
≤
1
,
∣
cos
x
∣
≤
1
∴
sin
x
+
cos
x
=
0
⇒
sin
(
x
+
4
π
)
=
0
⇒
x
+
4
π
=
nπ
⇒
x
=
nπ
−
4
π