How do we prove that $(1 - tan theta)/(1 + tan theta) = (cot theta - 1)/(cot theta + 1)$ ?

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Answer 1 · 2017-04-05T00:44:09

Use $tantheta = sintheta/costheta$ and $cottheta = costheta/sintheta$ .

$(1 - sintheta/costheta)/(1 +sintheta/costheta) = (costheta/sintheta - 1)/(costheta/sintheta + 1)$

$((costheta - sin theta)/costheta)/((costheta+ sin theta)/costheta) = ((costheta - sin theta)/sintheta)/((costheta + sin theta)/sintheta)$

$(costheta - sin theta)/(costheta + sin theta) = (costheta - sin theta)/(costheta + sin theta)$

This is true for all values of $theta$ , so we have proved this identity.

Hopefully this helps!

How do we prove that (1 - tan theta)/(1 + tan theta) = (cot theta - 1)/(cot theta + 1)(1 - tan theta)/(1 + tan theta) = (cot theta - 1)/(cot theta + 1)?