Question #7d769

1 Answer
Kevin D.
May 24, 2017

tan(A+B)-tan(A-B)=(2tanB)/(1-tan^2Atan^2B)

Explanation:

Use the trigonometric identity
tan(a+-b)=(tan(a)+-tan(b))/(1+--tan(a)tan(b))

So,
tan(A+B)=(tanA+tanB)/(1-tanAtanB)
tan(A-B)=(tanA-tanB)/(1+tanAtanB)
We will substitute:
a=tanA and b=tanB

So, tan(A+B)-tan(A-B)=(a+b)/(1-ab)-(a-b)/(1+ab)

(a+b)/(1-ab)-(a-b)/(1+ab)=((a+b)(1+ab)-(a-b)(1-ab))/(1-a^2b^2)
=(2b)/(1-a^2b^2)

Sub back:
tan(A+B)-tan(A-B)=(2tanB)/(1-tan^2Atan^2B)

Well... that's ugly but whatever.

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