Question : Find the value of $\frac{\cos^{2}25^\circ-\sin^{2}65^\circ}{\cos^{2}25^\circ+\sin^{2}65^\circ}$
Option 1: $\frac{1}{2}$
Option 2: $1$
Option 3: $–1$
Option 4: $0$
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Correct Answer: $0$
Solution :
Given:
$\frac{\cos^{2}25^\circ-\sin^{2}65^\circ}{\cos^{2}25^\circ+\sin^{2}65^\circ}$
= $\frac{\cos^{2}25^\circ-\sin^{2}(90^\circ-25^\circ)}{\cos^{2}25^\circ+\sin^{2}(90^\circ-25^\circ)}$
= $\frac{\cos^{2}25°-\cos^{2}25°}{\cos^{2}25°+\cos^{2}25°}$
= $\frac{0}{2\cos^{2}25^\circ}$
= $0$
Hence, the correct answer is $0$.
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