SOLUTION: Prove that (tanx)/(1+tanx)= 1/(1+cotx)

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Question 1202473: Prove that (tanx)/(1+tanx)= 1/(1+cotx)
Found 2 solutions by josgarithmetic, math_tutor2020:
Answer by josgarithmetic(39621) About Me  (Show Source):
You can put this solution on YOUR website!
tanx%2F%281%2Btanx%29

%28sinx%2Fcosx%29%2F%281%2Bsinx%2Fcosx%29

%28%28sinx%2Fcosx%29%2F%281%2Bsinx%2Fcosx%29%29%28%28cosx%2Fsinx%29%2F%28cosx%2Fsinx%29%29

%28%28sinx%2Fcosx%29%28cosx%2Fsinx%29%29%2F%28%281%2Bsinx%2Fcosx%29%28cosx%2Fsinx%29%29
and this should be enough for you to continue, and to finish.

Answer by math_tutor2020(3817) About Me  (Show Source):
You can put this solution on YOUR website!

I'll keep the left hand side (LHS) the same, while altering the right hand side (RHS)
The goal is to make the LHS and RHS expressions to be identical to each other.
%28tan%28x%29%29%2F%281%2Btan%28x%29%29+=+1%2F%281%2Bcot%28x%29%29

%28tan%28x%29%29%2F%281%2Btan%28x%29%29+=+1%2F%281%2B1%2Ftan%28x%29%29 Rewrite cot(x) as 1/tan

Multiply top and bottom by tan/tan, which is equivalent to 1.



Distribute in the denominator

%28tan%28x%29%29%2F%281%2Btan%28x%29%29+=+%28tan%28x%29%29%2F%28tan%28x%29%2B1%29

%28tan%28x%29%29%2F%281%2Btan%28x%29%29+=+%28tan%28x%29%29%2F%281%2Btan%28x%29%29

The identity has been confirmed.

If you wanted to alter the LHS, then keep the RHS the same. You could divide each piece of the LHS by tan(x) to effectively reverse the process shown above.