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`alpha ` is a root of equation `( 2 sin x - cos x ) (1+ cos x)=sin^2 x , beta ` is a root of the equation ` 3 cos ^2x - 10 cos x +3 =0 and gamma ` is a root of the equation `1-sin2 x = cos x- sin x : 0 le alpha , beta, gamma , le pi//2 ` `sin alpha + sin beta + sin gamma ` can be equal to

A

`(14-3sqrt(2))/( 6 sqrt(2))`

B

`5//6`

C

`(3+4sqrt(2))/(6)`

D

`(1+sqrt(2))/(2) `

Text Solution

Verified by Experts

The correct Answer is:
C
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