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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
2 years, 7 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.

- 2 years, 7 months ago

Ya I was talking of same non-bashing solution.Is there any shorter or equivalent method??

- 2 years, 7 months ago

That's the shortest and simplest solution according to me, I cannot think of any 'shorter' solution right now.

- 2 years, 6 months ago

According to me too .

- 2 years, 6 months ago