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Question
\[\frac{a \cos x + b \sin x + c}{\sin x}\]
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Solution
\[\frac{d}{dx}\left( \frac{a \cos x + b \sin x + c}{\sin x} \right)\]
\[ = \frac{d}{dx}\left( \frac{a \cos x}{\sin x} \right) + \frac{d}{dx}\left( \frac{b \sin x}{\sin x} \right) + \frac{d}{dx}\left( \frac{c}{\sin x} \right)\]
\[ = a\frac{d}{dx}\left( cot x \right) + \frac{d}{dx}\left( b \right) + c\frac{d}{dx}\left( \cos ec x \right)\]
\[ = - a \cos e c^2 x + 0 - c \cos ec x cot x\]
\[ = - a \cos e c^2 x - c \cos ec x cot x\]
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