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If 1+sinx+sin^2x+sin^3x+oo is equal to 4...

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

A

`pi/6`

B

`pi/4`

C

`pi/3or pi/6`

D

`pi/3 or (2pi)/3`

Text Solution

Verified by Experts

The correct Answer is:
D
Since `0ltxltpi." Therefore "sinxgt0`
We have `1+sinx+sin^2x+…oo=4+2sqrt3`
`rArr 1/(1-sinx)=4+2sqrt3` (sum of infinite G.P.)
`or sinx=1-1/(4+2sqrt3)=(3+2sqrt3)/(4+2sqrt3)=sqrt3/2`
`rArr x=pi/3or(2pi)/3`
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