6sin²(x-3π/2)-3√2 cosx=o

Question

6sin²(x-3π/2)-3√2 cosx=o

Answer 1

6sin²(x-3π/2)-3√2=0
6cos²x-3√2cosx=0
6cosx(cosx-√2/2)=0
cosx=0⇒x=π/2+πn
cosx=√2/2⇒x=+-π/4+2ππn

Answer 2

6(sinxcos3π/2-sin3π/2cosx)²-√3/2cosx=0
6cos²x-√3/2cosx=0
6cosx(cosx-√2/2)=0
6cosx=0
x=+-π/2+2πn, n∈Z
cosx=√2/2
cosx=√2/2
x=+-π/4+2πn, n∈Z