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Allied Angles

The value of ...

Question

The value of ${sin}^{2} \frac{5 π}{12} - {sin}^{2} \frac{π}{12}$ is

A

1 / 2

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B

\sqrt{3} / 2

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C

1

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D

0

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Solution

The correct option is B $\sqrt{3} / 2$
As we know that
$sin (a + b) sin (a - b) = {sin}^{2} a - {sin}^{2} b$

${sin}^{2} \frac{5 π}{12} - {sin}^{2} \frac{π}{12} = sin (\frac{5 π}{12} + \frac{π}{12}) sin (\frac{5 π}{12} - \frac{π}{12})$

$= sin \frac{6 π}{12} sin \frac{4 π}{12}$

$= sin \frac{π}{2} sin \frac{π}{3}$

$= sin \frac{π}{3}$

$= \frac{\sqrt{3}}{2}$

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