Department of Pre-University Education, KarnatakaPUC Karnataka Science Class 11

# A Cos X + B Sin X + C Sin X - Mathematics

$\frac{a \cos x + b \sin x + c}{\sin x}$

#### Solution

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

Concept: The Concept of Derivative - Algebra of Derivative of Functions
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#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 30 Derivatives
Exercise 30.3 | Q 11 | Page 34