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The value of $\sin 47 ° + \sin 61 ° - \sin 11 ° - \sin 25 °$ is

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$\cos 7 °$

$\sin 7 °$

$\cos 93 °$

$\sin 73 °$

answer is A.

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Detailed Solution

$\sin 47 ° + \sin 61 ° - \sin 11 ° - \sin 25 °$

$= 2 \sin 54 ° . \cos 7 ° - 2 \sin 18 ° . \cos 7 °$

$= 2 \cos 7 ° [\sin 54 ° - \sin 18 °]$

$= 2 \cos 7 ° [\frac{\sqrt{5} + 1}{4} - \frac{(\sqrt{5} - 1)}{4}]$

$= 2 \cos 7 ° [\frac{2}{4}] = \cos 7 °$

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