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प्रश्न
`int_(pi/5)^((3pi)/10) [(tan x)/(tan x + cot x)]`dx = ?
विकल्प
`(3pi)/10`
`pi/20`
`pi/2`
`pi/5`
MCQ
उत्तर
`pi/5`
Explanation:
Let I = `int_(pi/5)^((3pi)/10) (tan x)/(tan x + cot x)`dx
I = `int_(pi/5)^((3pi)/10) (tan ((3pi)/10 + pi/5 - x))/(tan ((3pi)/10 + pi/5 - x) + cot ((3pi)/10 + pi/5 - x))`
I = `int_(pi/5)^((3pi)/10) (cot x)/(cot x + tan x)`dx
2I = `int_(pi/5)^((3pi)/10) ((tan x + cot x)/(tan x + cot x)) "dx" = int_(pi/5)^((3pi)/10)`dx
I = `1/2((3pi)/10 - pi/5) = pi/20`
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