SOLUTION: Prove that: tan(45-x) = 1-tanx/1+tanx

Algebra ->  Trigonometry-basics -> SOLUTION: Prove that: tan(45-x) = 1-tanx/1+tanx      Log On


   

Question 976580: Prove that:
tan(45-x) = 1-tanx/1+tanx
Found 2 solutions by Edwin McCravy, FrankM:
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
Use the identity:

tan%28A-B%29%22%22=%22%22%28tan%28A%29-tan%28B%29%29%2F%281%2Btan%28A%29%2Atan%28B%29%29

substituting: A = 45°, B = x, and tan(45°) = 1

Edwin

Answer by FrankM(1040) About Me  (Show Source):
You can put this solution on YOUR website!
There is an identity for Tangent of the difference of 2 angles -
tan%28A-B%29=+%28tanA-tanB%29%2F%281%2BtanAtanB%29
here, A = 45, B = x, let's substitute :
tan%2845-x%29=+%28tan45-tanx%29%2F%281%2Btan45tanx%29
and one of the tan values I know by heart is tan 45 = 1. I hope you know this.
tan%2845-x%29=+%281-tanx%29%2F%281%2Btanx%29