$sin$ $(135^{o} + x) + sin (135^{o} x)$ equals

\sqrt{2} sin x

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\sqrt{3} cos x

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\sqrt{2} cos x

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\sqrt{3} sin x

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Solution

The correct option is B $\sqrt{2} cos x$
The value of $sin (135 + x) + sin (135 - x)$
$= \frac{cos x}{\sqrt{2}} - \frac{sin x}{\sqrt{2}} + \frac{cos x}{\sqrt{2}} + \frac{sin x}{\sqrt{2}}$
$= \sqrt{2} cos x$

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