Question

cos^43/2x-sin^43/2x=1/2

Answer 1

cos⁴((3/2)x)-sin⁴((3/2)x)=1/2
(cos²((3/2)x)-sin²((3/2)x))*(cos²((3/2)x)+sin²((3/2)x))=1/2
cos(3x)*1=1/2
cos(3x)=1/2
3x=+/-π/3+2πn
x₁,₂=+/-π/9+(2/3)πn.