Differentiate the following functions with respect to x :

$\frac{c o s (x - 2)}{s i n x}$

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Solution

We have,

$\frac{d}{d x} \frac{{c o s (x - 2)}}{s i n x}$

$= \frac{d}{d x} \frac{(c o s x . c o s 2 + s i n x . s i n 2)}{s i n x}$

$= c o s 2 \frac{d}{d x} (c o t x) + s i n 2 \frac{d}{d x} (1)$

$= - c o s 2. c o s e c^{2} x + 0$

$= - c o s e c 2 x c o s 2$

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