Question

Find the general solution of:

Cos²x.cosecx + 3sinx +3 =0

Answer 1

Answer:

cos^2 x / sin x + 3 sin x + 3 = 0

=> cos^2 x + 3 sin^2 x + 3sin x= 0

=> 1 + 2 sin^2 x + 3 sin x = 0

=> 2sin^2 x + 2 sin x + sinx + 1 = 0

=> (2sinx +1)(sinx + 1) = 0

Implies, either sin x= -1

or sin x = -1/2

So,

if sin x = -1

x = 2nπ + 3π/2

For all integers n

or,

sin x = -1/2 = sin (-π/6)

x = mπ +(-1)^m (-π/6)

or,

x = mπ -(-1)^m (π/6)

for every integer m.

This will be the general solution for x in this question.

Hope this helps you !

Answer 2

Answer:

hope it's helpful

Step-by-step explanation:

cos²x.cosecx+3sinx+3=0

thanks