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$\int_{0}^{π / 2} \frac{5 \tan x - 3 \cot x}{\tan x + \cot x} d x =$

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a

π2

b

π3

c

π4

d

π8

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detailed solution

Correct option is A

I=∫0π/2 5tan⁡x−3cot⁡xtan⁡x+cot⁡xdx------1I=∫0π/2 5tan⁡π2−x−3cot⁡π2−xtan⁡π2−x+cot⁡π2−xdxI=∫0π/2 5cot⁡x−3tan⁡xcot⁡x+tan⁡xdx----2(1)+(2)⇒2I=∫0π/2 2tan⁡x+2cot⁡xcot⁡x+tan⁡xdx=∫0π/2 2dx=2∫0π/2 (1)dx=2(x)0π/2=2π2=π⇒I=π2

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