Trig equation help! Emergency! tan2x = cosx?

Answer 1

sin 2x /cos 2x = cos x
sin 2x = cos x cos 2x
2 sin x cos x = cos x cos 2x
2 sin x cos x - cos x cos 2x = 0
cos x(2 sin x - cos 2x) = 0
cos x (2 sin ² x + 2 sin x - 1) = 0
cos x = 0
x = 90° , 270°
sin x = [- 2 ± √(4 + 8) ] / 4
sin x = [ - 2 ± 2√3) ] / 4
sin x = - 1/2 ± (1/2)√(3)
sin x = (-1/2) (1 ± √3)
sin x = (-1/2) (2.732) , sin x = (-1/2)(- 0.732)
Accept 2nd answer for sin x:-
sin x = 0.366
x = 21.5° , 159°

Answers are 90° , 270° , 21.5°, 159°

Answer 2

tan2x = cosx
sin2x/cos2x = cosx
2sinx cosx = cosx cos2x
2sinx cosx - cosx(1-2sin^2x) =0
cosx( 2sin^2x +2sinx -1)=0
cosx =0 or sinx = (-2 +/- sqr(12))/4
cosx =0 or sinx = (-1 +/- sqr(3))/2
ie cos x=0 or sinx = (sqr(3)-1)/2
x = (2n+1)pi/2 or x = npi +(-1)^n arsin((sqr(3)-1)/2) n E J