SOLUTION: Using tanx=sinx/cosx, prove the addition formula for tangent, tan(A+B)=(tanA+tanB)/(1-tanAxtanB).

Algebra ->  Algebra  -> Trigonometry-basics -> SOLUTION: Using tanx=sinx/cosx, prove the addition formula for tangent, tan(A+B)=(tanA+tanB)/(1-tanAxtanB).       Log On

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Question 196593: Using tanx=sinx/cosx, prove the addition formula for tangent, tan(A+B)=(tanA+tanB)/(1-tanAxtanB).

Answer by jim_thompson5910(21685) About Me  (Show Source):
You can put this solution on YOUR website!
Since tan%28x%29=sin%28x%29%2Fcos%28x%29, we can say


tan%28A%2BB%29=sin%28A%2BB%29%2Fcos%28A%2BB%29

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tan%28A%2BB%29=sin%28A%2BB%29%2Fcos%28A%2BB%29 Start with the given equation.


tan%28A%2BB%29=%28sin%28A%29cos%28B%29%2Bcos%28A%29sin%28B%29%29%2Fcos%28A%2BB%29 Expand sine using the sum difference identity


tan%28A%2BB%29=%28sin%28A%29cos%28B%29%2Bcos%28A%29sin%28B%29%29%2F%28cos%28A%29cos%28B%29-sin%28A%29sin%28B%29%29 Expand cosine using the sum difference identity


tan%28A%2BB%29=%28%28sin%28A%29cos%28B%29%29%2Fcos%28A%29%2B%28cos%28A%29sin%28B%29%29%2Fcos%28A%29%29%2F%28%28cos%28A%29cos%28B%29%29%2Fcos%28A%29-%28sin%28A%29sin%28B%29%29%2Fcos%28A%29%29 Divide EVERY term by cos%28A%29


tan%28A%2BB%29=%28tan%28A%29cos%28B%29%2Bsin%28B%29%29%2F%28cos%28B%29-tan%28A%29sin%28B%29%29 Reduce and simplify


tan%28A%2BB%29=%28%28tan%28A%29cos%28B%29%29%2Fcos%28B%29%2Bsin%28B%29%2Fcos%28B%29%29%2F%28cos%28B%29%2Fcos%28B%29-%28tan%28A%29sin%28B%29%29%2Fcos%28B%29%29 Divide EVERY term by cos%28B%29


tan%28A%2BB%29=%28tan%28A%29%2Btan%28B%29%29%2F%281-tan%28A%29tan%28B%29%29 Reduce and simplify



So this verifies tan%28A%2BB%29=%28tan%28A%29%2Btan%28B%29%29%2F%281-tan%28A%29tan%28B%29%29