The value of `x` in `(0,pi/2)` satisfying `(sqrt(3)-1)/(sinx)+(sqrt(3)+1)/(cosx)=4sqrt(2) ` is / are

Explanation

`(sqrt3 - 1)/sinx +(sqrt3+1)/cosx = 4sqrt2`

`=>(sqrt3 - 1) cosx +(sqrt3 + 1)sinx = 4sqrt2 sinxcosx`

`=>(sqrt3 - 1)/(2sqrt2) cosx +(sqrt3 + 1)/(2sqrt2)sinx = 2 sinxcosx`

Now, we know, `(sqrt3 - 1)/(2sqrt2) = sin(pi/12) and (sqrt3 + 1)/(2sqrt2) = cos(pi/12)`

So, our equation becomes,

`=>sin(x+pi/12) = sin2x`

`=>2x = npi+(-1)^n (x+pi/12)`

When `n = 0`

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