Evaluate : ∫ \frac{cos2x+2sin^2x}{\cos^2x} dx

CBSE Class 12 Math 2018 Solved Paper - Question 9

Question : 9 of 29

Marks: +1, -0

Evaluate : ∫

{cos2x+2sin^2x}/{cos^2x}

Solution:

Given I = ∫

{cos2x+2sin^2x}/{cos^2x}

dx
I =

{cos^2x-sin^2x+2sin^2x}/{cos^2x}

dx ... (Since cos 2x =

cos^2x - sin^2x

)
I = ∫

{cos^2x+sin^2x}/{cos^2x}

dx
I = ∫

sec^2

x dx
I = tan x + C

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