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$\int \frac{\sec x d x}{\sqrt{\cos 2 x}} =$

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sin−1⁡(tan⁡x)+c

tan⁡x+c

cos−1⁡(tan⁡x)+c

sin⁡xcos⁡x+c

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detailed solution

Correct option is A

∫sec⁡xdxcos⁡2x=∫sec⁡xcos2⁡x−sin2⁡xdx =∫sec2⁡xdx1−tan2⁡xlet tanx=t sec2xdx=dt=sin−1⁡(tan⁡x)+c

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