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Number of principal solution(s) of the equation sqrt(sin x) -1/(sqrt(sin x))= cos x, is :

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SOLUTION :`sqrt(SIN x) -1/(sqrt(sin x))= COS x`
`sin x + 1/(sin x) -2 = cos^(2)x = (1-sin^(2)x)`
Let `sin x = t`
`t + 1/t -2 = 1 - t^(2)`
`t^(2) - 2t + 1 = t(1-t)(1+t)`
`implies (1-t)[(1-t)-t(1+t)] = 0`
`implies (1-t)[1-2t-t^(2)] = 0`
`t = 1,t^(2) + 2t -1 = 0`
`sin x = 1, sin x = (-2+-sqrt(4+4))/(2)`
`sin x = 1, implies x = (pi)/2`
also `sin x = sqrt(2)-1 and cos x lt 0`
`implies` ONE solution in `(0,2 pi)`.


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