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Q.

The value of $\sin^{2} (52 \frac{1}{2}) ° - \sin^{2} (22 \frac{1}{2}) °$ is

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a

$\frac{\sqrt{3} + 1}{\sqrt{2}}$

b

$\frac{\sqrt{3} + 1}{4 \sqrt{2}}$

c

$\frac{\sqrt{3} - 1}{4 \sqrt{2}}$

d

$\frac{\sqrt{3} + 1}{4}$

answer is A.

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Detailed Solution

$\sin^{2} (52 \frac{1}{2}) ° - \sin^{2} (22 \frac{1}{2}) °$

$= \sin (52 \frac{1}{2} + 22 \frac{1}{2}) \sin (52 \frac{1}{2} - 22 \frac{1}{2})$

$= \sin 75 ° \cdot \sin 30 °$

$= \frac{\sqrt{3} + 1}{2 \sqrt{2}} \times \frac{1}{2}$

$= \frac{\sqrt{3} + 1}{4 \sqrt{2}}$

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