prove that cos3x+sin3x/cos x-sin x=1+2sin2x

Answer 1

Do not omit required parentheses:
Prove:
(cos3x+sin3x)/(cos x-sin x)=1+2sin2x
Have you tried using multiple angle formulae:
sin(2A)=2sin(A)cos(A)
cos(2A)=cos²(A)-sin²(A)
sin(3A)=3sin(A)-4sin³(A)
cos(3A)=4cos³(A)-3cos(A)
and possibly
sin²(A)+cos²(A) = 1