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CBSE Class 12 Math 2018 Solved Paper

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Question : 9 of 29
Marks: +1, -0
Evaluate : ∫ cos⁡2x+2sin⁡2xcos⁡2x\frac{\cos 2x + 2\sin^2 x}{\cos^2 x} dx
Solution:  
Given I = ∫ cos⁡2x+2sin⁡2xcos⁡2x\frac{\cos 2x + 2\sin^2 x}{\cos^2 x} dx
I = cos⁡2x−sin⁡2x+2sin⁡2xcos⁡2x\frac{\cos^2 x - \sin^2 x + 2\sin^2 x}{\cos^2 x} dx ... (Since cos 2x = cos⁡2x−sin⁡2x\cos^2 x - \sin^2 x)
I = ∫ cos⁡2x+sin⁡2xcos⁡2x\frac{\cos^2 x + \sin^2 x}{\cos^2 x} dx
I = ∫ sec⁡2\sec^2 x dx
I = tan x + C
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