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need solution for rd sharma maths class 12 chapter Indefinite integrals exercise 18.1 question 5 sub question (ii)

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Answer: \tan x+c

Hint: You must know trigonometric identities

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

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

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

                =\int \frac{1}{\cos ^{2}x}dx=\int \sec ^{2}x\; dx                                    \left ( \because \frac{1}{\cos x}=\sec \; x \right )        

                =\tan x+c

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