find general solution of cot^2x + 3/sinx +3=0
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Find the general solution: cot
2
x+
sinx
3
+3=0
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ANSWER
Given equation is cot
2
x+
sinx
3
+3=0
⇒
sin
2
x
cos
2
x
+
sinx
3
+3=0
⇒
sin
2
x
1−sin
2
x
+
sinx
3
+3=0
⇒(1−sin
2
x)+3sinx+3sin
2
x=0
(sinx
=0).
⇒2sin
2
x+3sinx+1=0
⇒2sin
2
x+2sinx+sinx+1=0
⇒(2sinx+1)(sinx+1)=0
⇒sinx=
2
−1
or sinx=−1
⇒x=nπ+(−1)
n
(
6
−π
) and x=nπ+(−1)
n
(
2
−π
)
where n=0,1,2,3,...
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