Question

Sin³x cosx - cos³x sin x = √3 / 8

Answer 1

sin³x·cos x - cos³x·sin x = √3/8

sin x·cos x·(sin²x - cos²x) = √3/8

1/2 · sin 2x · (-cos 2x) = √3/8

2 · sin 2x · (-cos 2x) = √3/2

sin 4x = -√3/2

4x = (-1)ⁿ⁺¹·π/3 + πn, n ∈ Z

x = (-1)ⁿ⁺¹·π/12 + πn/4, n ∈ Z