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HELP ME, PLEASE. I REALLY NEED IT Find x: S=(1)/(sin2x)+(1)/(sin4x)+(1)/(sin8x)+...+(1)/(sin2^(n)x )
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Mar 26, 2021
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HELP ME, PLEASE. I REALLY NEED IT
Find x:
Mathematics
high-school
Paul J Abernathy
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Answer:
cotx - cot2ⁿx
Explanation:
Note: finding the sum not x
First rewrite the first term as:
1/sin2x =
sinx / (sinxsin2x) =
sin(2x-x) / (sinxsin2x) =
(sin2xcosx - cosxsinx) / (sinxsin2x) =
(sin2xcosx)/(sinxsin2x) - (cos2xsinx)/(sinxsin2x) =
cosx/sinx - cos2x/sin2x =
cotx - cot2x
Now the sum is:
S = cotx - cot2x + cot2x - cot4x +... + cot2ⁿ⁻²x - cot2ⁿx =
cotx - cot2ⁿx
Lakhan Sharma
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Apr 2, 2021
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Lakhan Sharma
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