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If $f (x) = cosec (x + π / 3) cosec (x + π / 6)$ then the value of $\int_{0}^{π / 2} f (x) d x$ is

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2 log 3

– 2 log 3

log 3

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detailed solution

Correct option is A

I=∫0π/2 cosec⁡(x+π/3)cosec⁡(x+π/6)dx=1sin⁡(π/6)∫0π/2 sin⁡[(x+π/3)−(x+π/6)sin⁡(x+π/3)sin⁡(x+π/6)dx=2∫0π/2 [cot⁡(x+π/6)−cot⁡(x+π/3)]dx=2log⁡sin⁡(x+π/6)sin⁡(x+π/3)0π/2=2log⁡3/21/2−log⁡1/23/3=2log⁡3

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If f(x)=cosec⁡(x+π/3)cosec⁡(x+π/6) then the value of ∫0π/2 f(x)dx is

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If $f (x) = cosec (x + π / 3) cosec (x + π / 6)$ then the value of $\int_{0}^{π / 2} f (x) d x$ is