What is the value of \(\displaystyle\frac{\cos^2 34^\circ+\cos^2 56^\circ}{\sin^2 30^\circ}\)?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 4
Since \(34^\circ+56^\circ=90^\circ\), \(\cos 56^\circ=\sin 34^\circ\), and the numerator becomes \(\cos^2 34^\circ+\sin^2 34^\circ\).
Numerator \(=\cos^2 34^\circ+\sin^2 34^\circ=1\)
\(\sin^2 30^\circ=\left(\displaystyle\frac{1}{2}\right)^2=\frac{1}{4}\)
\(\displaystyle\frac{1}{1/4}=4\)