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int(0)^(pi//6)(sinx)/(cos^(3)x) dx is eq...

`int_(0)^(pi//6)(sinx)/(cos^(3)x) dx` is equal to

A

`(2)/(3)`

B

`(1)/(6)`

C

2

D

`(1)/(3)`

Text Solution

Verified by Experts

The correct Answer is:
B
Let ` l = int_(0)^(pi//6) (sinx)/(cos^(3)x) dx`
Put `cos x= t rArr -sin x dx = dt `
` :. l = - int_(1)^(sqrt(3))(1)/(t^(3))dt=[(1)/(2t^(2)]]_(1)^(sqrt3//2) = 1/6`
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