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The value of x in (0,pi/2) satisfying th...

The value of x in `(0,pi/2)` satisfying the equation, `(sqrt3-1)/sin x+ (sqrt3+1)/cosx=4sqrt2` is -

A

`pi/12`

B

`(5pi)/12`

C

`(7pi)/24`

D

`(11 pi)/36`

Text Solution

Verified by Experts

The correct Answer is:
A, D
`(sqrt(3)-1)/(2sqrt(2) sin x)+(sqrt(3)+1)/(2sqrt(2) cos x)=2`
`"sin" pi/12 cos x + "cos" pi/12 sin x= sin 2x`
`sin 2x= sin (x+pi/12)`
`:. 2x=x+pi/12 or 2x=pi-x- pi/12`
`x=pi/12 ot 3x=pi/12`
`:. X=pi/12 or (11 pi)/36`
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