I came across a problem which said prove using only Pythagorean Identities and I got stumped. Some Insight would be helpful.
$$\cos^5(a)=\cos(a)-2\sin^2(a)\cos(a)$$
What I first did was factor the right side and used the main pythagorean identity to try and simplify but I don't really think it got me anywhere. My final step somehow got me to;
$$\cos^2(a)-\sin^2(a)=\cos^4(a)$$
Where do I go from there or what could I have done differently in the start?