Question

prove that 1+cos^2x =2(cos^4x+sin^4x)​

Answer 1

RHS

2(cis^4x + sin^4x)

2{(cos^2x+sin^2x)^2-2sin^2(2x)}

2{1-2sin^2(2x)}

LHS

1+cos^2(2x)

2(1-2sin^2(2x))

so LHS=RHS

prove

Answer 2

Solutions:

x = π n, n element Z

x = π n - (2 π)/3, n element Z

x = π n - (4 π)/3, n element Z