Question

Prove identity: tanx-1/tanx+1= 1-cotx/1+cotx

Answer 1

tanx = sinx/cosx
Hence
tanx-1/tanx+1 = (sinx/cosx)-1/(sinx/cosx)+1
Hence
(sinx/cosx)-1/(sinx/cosx)+1 = ((sinx-cosx)/cosx)/((sinx+cosx)/cosx)
Can you go from here?

Answer 2

Just one substitution and you will be there:
Just use:
\[\tan(x) = \frac{1}{\cot(x)}\]

Answer 3

^ True. My way is 10x more complicated.

Answer 4

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