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if 1+sin theta+sin 2 theta+.....infinity=4+2root3 where 0 then theta=??? pls very urgent

if 1+sin theta+sin2theta+.....infinity=4+2root3 
where 0
then theta=???
pls very urgent

Grade:12th Pass

1 Answers

Arun
25763 Points
4 years ago
When we see in LHS
This is a GP of infinite terms
Hence
Sum of GP of infinite terms = 1/(1- sin\large \theta)
But 
1/(1-sin\large \theta) = 4 + 2\large \sqrt3
1- sin\large \theta = (4 - 2\large \sqrt3)/(16-12)
1- sin\large \theta = (2 - \large \sqrt3) / 2
2 Sin\large \theta = \large \sqrt3
Sin \large \theta = \large \sqrt3 /2
As we know
Sin\large \theta = Sin 60
Hence 
\large \theta = 60 degree

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