[Math] Prove the identity $\sin^4α-\cos^4α=2\sin^2α-1$

Question

Prove the identity $\sin^4α-\cos^4α=2\sin^2α-1$

Well, I thought to start it this way:
$$(\sin^2α-\cos^2α)(\sin^2α+\cos^2α)=2\sin^2α-1=>\\(\sin α-\cos α)(\sin α+\cos α)(\sin^2α+\cos^2α)=2\sin^2α-1$$ I don't know how to continue…

Answer 1

Hint: $ \sin^2 \alpha + \cos^2\alpha=1 $ substituting in the two sides you have the identity.