What is the value of \(\sin^2 21^\circ+\sin^2 69^\circ\)?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 1
The angles \(21^\circ\) and \(69^\circ\) add up to \(90^\circ\), so \(\sin 69^\circ=\cos 21^\circ\). The sum then becomes \(\sin^2+\cos^2\) of one angle.
\(\sin 69^\circ=\sin(90^\circ-21^\circ)=\cos 21^\circ\)
\(\sin^2 21^\circ+\cos^2 21^\circ=1\)