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alpha is a root of the equation (2sinx-c...

`alpha` is a root of the equation `(2sinx-cosx)(1+cosx)=sin^2x`
`beta` is a root of the equation `3cos^2x-10cosx+3=0` and `gamma` is a root of the equation 1-sin2x=cosx-sinx where `0 le alpha, beta, gamma le pi//2`
Answer the following question on above passage:
`sinalpha+sinbeta+singamma` can be equal

A

`(14+3sqrt2)/(6sqrt2)`

B

44322

C

`(3+4sqrt2)/6`

D

`(1+sqrt2)/6`

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The correct Answer is:
A
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