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Please solve rd sharma class 12 chapter Indefinite integrals exercise 18.1 question 5 sub question (i) maths textbook solution

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Answer: -\cot x+c

Hint: You must know trigonometric identities.

Given: \int \frac{\cos 2x+2\sin ^{2}x}{\sin ^{2}x}dx

Solution: \int \frac{\cos 2x+2\sin ^{2}x}{\sin ^{2}x}dx

                =\int \frac{1-2\sin ^{2}x+2\sin ^{2}x}{\sin ^{2}x}dx                    \left ( \because \cos 2x=1-2\sin ^{2}x \right )

                =\int \frac{1}{\sin ^{2}x}dx=\int \cos e\: c^{2}\; x\: dx                \left ( \because \frac{1}{\sin x} =cosec\; x\right )

                =-\cot \; x+c

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