Question

Use the Pythagorean Identities to simplify: cot^2 theta - cot^2 theta cos^2 theta and (cos x + sin x)^2

Answer 1

lets put \(a=\cos(\theta)\) and \(b=\sin(\theta)\) then
\[(a+b)^2=a^2+b^2+2ab\] and since \(\cos^2(\theta)+\sin^2(\theta)=1\) you get
\[a^2+b^2+2ab=1+2ab=1+2\sin(\theta)\cos(\theta)\]