SOLUTION: verify the identity step by step cot3x=1-tan^2x/3tanx-tan^3x

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Question 300647: verify the identity step by step
cot3x=1-tan^2x/3tanx-tan^3x

Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
Cot3x=%281-Tan%5E2x%29%2F%283%2ATanx-Tan%5E3x%29

Sorry, but that is not an identity, for let x = 45°



Cot%28%22135%B0%22%29=%281-1%5E2%29%2F%283%281%29-%281%29%5E3%29

-1=0

That's false, so it isn't an identity!

However, a correct identity, which is just like what you posted 
but has a -3 coefficient for the second factor in the top on the
right instead of -1 is given below, which makes me think this
is what it should have been:

Cot3x=%281-3%2ATan%5E2x%29%2F%283%2ATanx-Tan%5E3x%29

1%2F%28Tan%283x%29%29=%22%22

1%2FTan%282x%2Bx%29=%22%22

1%2F%28%28Tan%282x%29%2BTan%28x%29%29%2F%281-Tan%282x%29Tan%28x%29%29%29=%22%22

1%22%F7%22%28%28Tan%282x%29%2BTan%28x%29%29%2F%281-Tan%282x%29Tan%28x%29%29%29=%22%22

1%22%D7%22%28++%281-Tan%282x%29Tan%28x%29%29%2F%28Tan%282x%29%2BTan%28x%29%29%29=%22%22

++%281-Tan%282x%29Tan%28x%29%29%2F%28Tan%282x%29%2BTan%28x%29%29=%22%22





Multiply every term on top and bottom by LCD = 1-Tan%5E2x



%281-Tan%5E2x-2Tan%5E2x%29%2F%282Tan%28x%29%2BTan%28x%29-Tan%5E3x%29=%22%22

%281-3Tan%5E2x%29%2F%283Tan%28x%29-Tan%5E3x%29=%22%22

Edwin