How do I solve?

5 sin 4x = - 10 sin 2x

Solve 5sin 4x = - 10sin 2x

Ans: 0, pi/2, pi

Explanation:

sin 4x = 2sin 2x. cos 2x

10sin 2x. cos 2x + 10sin 2x = 0

10sin 2x (cos 2x + 1) = 0

a. sin 2x = 0 - - >

2x = 0 - - > x = 0

2x = pi - - > x = pi/2

2x = 2pi x = pi

b. cos 2x = - 1 - - > 2x = pi - - > x = pi/2

Move 5cos (x) 5cos (x) to the left side of the equation by subtracting it from both sides. 5sin (2x) - 5cos (x) = 0 5sin (2x) - 5cos (x) = 0 Simplify each term. Apply the sine double-angle identity. 5 (2sin (x) cos (x)) - 5cos (x) = 0 5 (2sin (x) cos (x)) - 5cos (x) = 0 Multiply 22 by 55 to get 1010. 10 (sin (x) cos (x)) - 5cos (x) = 0 10 (sin (x) cos (x)) - 5cos (x) = 0 Remove parentheses around sin (x) cos (x) sin (x) cos (x). 10sin (x) cos (x) - 5cos (x) = 0 10sin (x) cos (x) - 5cos (x) = 0 Factor 5cos (x) 5cos (x) out of 10sin (x) cos (x) - 5cos (x) 10sin (x) cos (x) - 5cos (x).

Factor 5cos (x) 5cos (x) out of 10sin (x) cos (x) 10sin (x) cos (x). 5cos (x) (2sin (x)) - 5cos (x) = 0 5cos (x) (2sin (x)) - 5cos (x) = 0 Factor 5cos (x) 5cos (x) out of - 5cos (x) - 5cos (x). 5cos (x) (2sin (x)) + 5cos (x) (-1) = 0 5cos (x) (2sin (x)) + 5cos (x) (-1) = 0 Factor 5cos (x) 5cos (x) out of 5cos (x) (2sin (x)) + 5cos (x) ⋅-1 5cos (x) (2sin (x)) + 5cos (x) ⋅-1. 5cos (x) (2sin (x) - 1) = 0