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.

#Geometry #Trigonometry #Tangent #Proofs #Bash

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Comments

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 - 5 years, 11 months ago

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

shivamani patil - 5 years, 11 months ago

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

Krishna Sharma - 5 years, 11 months ago

@Krishna Sharma – According to me too .

shivamani patil - 5 years, 11 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$