What is (\sin^4 x+\cos^4 x) equal to?

Correct answer: \(1-2\sin^2 x\cos^2 x\)

Using \(a^2+b^2=(a+b)^2-2ab\), take \(a=\sin^2 x\) and \(b=\cos^2 x\). Then \(\sin^4 x+\cos^4 x=(\sin^2 x+\cos^2 x)^2-2\sin^2 x\cos^2 x\). Since \(\sin^2 x+\cos^2 x=1\), the expression equals \(1-2\sin^2 x\cos^2 x\). Option A incorrectly has a plus sign instead of a minus sign. Exam tip: for fourth powers, treat \(\sin^2 x\) and \(\cos^2 x\) as the two terms before applying an algebraic identity.