Question

how to solve: sin4x+sin2x=cosx

Answer 1

do you want to prove it or want to solve it for the value of theta?

Answer 2

use sin2x=2sinx cosx
1+cos2x=2cos^2 x

Answer 3

use the identity :
sinA + sinB = 2sin((A+B)/2)cos((A-B)/2)

Answer 4

let A = 4x and B = 2x
see the equation above becomes
2sin3xcosx = cosx
2sin3xcosx - cosx = 0
factor out!
cosx(2sin3x - 1) = 0
set each factor be zero then solve for x

Answer 5

Thanks RadEn, I was forgetting to factor the equation. It is solved now.

Answer 6

you;re welcome