SOLUTION: Can you please help me to prove a tangent subtraction identity tan(a-b)=(tana-tanb)/(1+tana*tanb) using geometric techniques? Thank you so much!

Question 373748: Can you please help me to prove a tangent subtraction identity tan(a-b)=(tana-tanb)/(1+tana*tanb) using geometric techniques?
Thank you so much!
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

I don't know of a direct geometric proof of the tangent of a difference formula. I've always seen it done by geometric proofs of

and

and then using

Geometric proofs of the sine and cosine of differences can be found at:

Sine and Cosine of Difference Proofs

Then the algebra to get it into the final form for tangent is found at:

Sum/Difference Formulas (Scroll Down to TANGENT A�B)

John

My calculator said it, I believe it, that settles it

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