#### Need solution for rd sharma maths class 12 chapter Indefinite Integrals exercise 18.2 question 27

$-(cosec x + cot x +x)+c$

Hint: To solve this equation we add $cosec x + cot x$

\begin{aligned} &\text { Given: } \int \frac{\cot x}{\cos e c x-\cot x} d x \\ &\text { Solution: } \int \frac{\cot x}{\cos e c x-\cot x} d x \end{aligned}

$\\ \\ \frac{\cot x}{\cos ec x -\cot x}\times \frac{\cos ec x+\cot x}{\cos ec x+\cot x}=\cot x\cdot \cos ec x+\cot^{2}x \\ \\ \Rightarrow \hspace{1cm}I=\int (\cot x \cdot \cos ec x)dx+\int (\cos ec^{2}x-1)dx \\ \\ \Rightarrow \hspace{1cm}I=-\cos ec x -\cot x+c$