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" 1श्न 8."int(pi/6)^( pi/3)(sqrt(tan x))...

" 1श्न 8."int_(pi/6)^( pi/3)(sqrt(tan x))/(sqrt(tan x)+sqrt(cot x))dx=(pi)/(12)

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int_(0)^((pi)/(2))(sqrt(tan x))/(sqrt(tan x+sqrt(cot x)))dx

int_(0)^((pi)/(2))(sqrt(cot x))/(sqrt(tan x)+sqrt(cot x))dx=

int_(0)^((pi)/(2))(4sqrt(cot x))/(4sqrt(tan x) + 4sqrt(cot x)) dx

int_(pi//6)^(pi//3) (dx)/(1 + sqrt(tan x)) =

Prove that :int(sqrt(tan x))/(sqrt(tan+sqrt(cot x)))=(pi)/(4)

int_(0)^((pi)/(4))sqrt(tan x)dx

int_0^(pi//2) (sqrt( cot x))/(sqrt(cot x) - sqrt(tan x)) dx is :

int_(0)^(pi//2)(1)/(sqrt(tan x)-sqrt(cot x))dx=