If `1+sinx+sin^2x+sin^3x+oo` is equal to `4+2sqrt(3),0

Options

A. `(pi)/3,(5pi)/6`
B. `(2pi)/3,(pi)/6`
C. `(pi)/3,(2pi)/3`
D. `(pi)/6,(pi)/3`

Answer

C

Explanation

Given
`1+sin x +sin^(2) x =……….oo =4+2sqrt(3)`
`implies 1/(1-sinx)=4+2sqrt(3)`
`implies1-sin x=1/(4+2sqrt(3))xx(4-2sqrt(3))/(4-2sqrt(3))`
`implies 1-sin x=(4-2sqrt(3))/4`
`impliessinx =(2sqrt(3))/4=(sqrt(3))/2`
`implies x=(pi)/3,(2pi)/3`