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Bashing available and also unavailable:Proving a trigonometric result

I was studying trigonometry and I found a good prove problem which is

Prove that:\(\tan { A } +2\tan { 2A } +4\tan { 4A } +8\cot { 8A } =\cot { A } \).

I have a non-bashing solution,want to see your approach.

Note by Shivamani Patil
1 year, 6 months ago

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Take tan on RHS and use the property

\(\displaystyle cotA - tanA = 2cot(2A)\)

Again take 2tan2A on RHS

\(2cot2A - 2tan2A = 4cot4A\)

Again bring 4tan4A on RHS

\(4cot4A - 4tan4A = 8cot8A\) on RHS

I think there is a typo it should be 8cot8A instead of 8tan8A on LHS. Krishna Sharma · 1 year, 6 months ago

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@Krishna Sharma Ya I was talking of same non-bashing solution.Is there any shorter or equivalent method?? Shivamani Patil · 1 year, 6 months ago

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@Shivamani Patil That's the shortest and simplest solution according to me, I cannot think of any 'shorter' solution right now. Krishna Sharma · 1 year, 6 months ago

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@Krishna Sharma According to me too . Shivamani Patil · 1 year, 6 months ago

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