Given that \(\sin\) \(+ \cos\ \) \( = q\), show that \(sin^4\ \) \(+ \cos^4\ \) \( =\) \(\frac{2 - (q^2 - 1)^2}{2}\).
Proof:
Given \(\sin\ \) \(+ \cos\ \) \(= q\)
Squaring on both sides.
\((\sin\ \) \(+ \cos\ \) \()^2 = q^2\)
\(\sin^2\ \) \(+ \cos^2\ \) \(+ 2\sin\ \) \(\cos\ \) \(= q^2\)
Hence proved.