Question : Evaluate the expression: $\frac{\sin ^2 63^{\circ}+\sin ^2 27^{\circ}}{\cos ^2 17^{\circ}+\cos ^2 73^{\circ}}$
Option 1: 0
Option 2: 3
Option 3: 1
Option 4: 2
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Correct Answer: 1
Solution :
$\frac{\sin ^2 63^{\circ}+\sin ^2 27^{\circ}}{\cos ^2 17^{\circ}+\cos ^2 73^{\circ}}$
= $\frac{\sin ^2 63^{\circ}+\sin ^2 (90^{\circ}-63^{\circ})}{\cos ^2 17^{\circ}+\cos ^2 (90^{\circ}-17^{\circ})}$
= $\frac{\sin ^2 63^{\circ}+\cos ^2 63^{\circ}}{\cos ^2 17^{\circ}+\sin ^2 17^{\circ}}$
= $\frac{1}{1}$
= 1
Hence, the correct answer is 1.
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