Question

Prove that
2cos^(2)x + 3sinx= 0

Answer 1

Answer:

x = 30° + 360°k  OR   x = 150° + 360°k,  where k is an integer.

Step-by-step explanation:

Assuming you mean solve this equation (it's not a true identity to be proved)...

2 cos² x + 3 sin x = 0

=> 2 ( 1 - sin² x ) + 3 sin x = 0

=> 2 - 2 sin² x + 3 sin x = 0

=> 2 sin² x - 3 sin x - 2 = 0

=> ( 2 sin x + 1 ) ( sin x - 2 ) = 0

=> sin x = -1/2  OR   sin x = 2

But sin x cannot be greater than 1, so

sin x = -1/2

=> x = 30° + 360°k  OR   x = 150° + 360°k,  where k is an integer.