Question 57
Find the value of $$\frac{\cos^2 30^\circ - \sin^2 30^\circ}{\sin^2 15^\circ + \cos^2 15^\circ}$$
Solution
$$\frac{\cos^230^{\circ}-\sin^230^{\circ}}{\sin^215^{\circ}+\cos^215^{\circ}}=\frac{\left(\frac{\sqrt{3}}{2}\right)^2+\left(\frac{1}{2}\right)^2}{1}=\frac{3}{4}-\frac{1}{4}=\frac{2}{4}=\frac{1}{2}$$
Hence, the correct answer is Option D
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