Question

Sin*2x -2cos x+1/4=0

Answer 1

Hi ,

Sin²x -2cosx + 1/4 = 0

Multiply each term with 4

4sin²x - 8cosx + 1 = 0

4( 1 - cos² x ) - 8cosx + 1 = 0

4 - 4cos²x - 8cosx + 1 = 0

-4cos² x - 8cosx +5 = 0

-4cos² x -10cosx + 2cosx + 5 = 0

-2cosx ( 2cosx + 5 ) + ( 2cosx + 5 ) = 0

( 2cosx + 5 ) ( -2cosx + 1 ) = 0

Therefore ,

2cosx + 5 = 0 or -2cosx + 1 = 0

cosx = -5/2 or cosx = 1/2

Cosx = 1/2

Cosx = cos 30°

x = 30°

I hope this helps you.

:)

Answer 2

1-cos*2x- 2cosx+1/4=0
cos*2x + 2cosx-5/4=0
(cosx +1)*2 -5/4-1=0
(cosx+1)*2 -9/4=0
(cosx+1)*2 =9/4
taking square root
cosx +1=+3/2 or cosx +1=-3/2
cosx =1/2. or cosx = -5/2
x=60°. or not possible