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Question
cos (x + a)
Solution
\[\frac{d}{dx}\left[ \cos \left( x + a \right) \right]\]
\[ = \frac{d}{dx}\left( \cos x \cos a - \sin x \sin a \right)\]
\[ = \cos a\frac{d}{dx}\left( \cos x \right) - \sin a \frac{d}{dx}\left( \sin x \right)\]
\[ = - \cos a \sin x - \sin a \cos x\]
\[ = - \left( \sin x \cos a + \cos x \sin a \right)\]
\[ = - \sin\left( x + a \right)\]
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