Question

find general solution of cot^2x + 3/sinx +3=0​

Answer 1

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,...