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

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

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-(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

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