How do you prove $(1-tantheta)/(1+tantheta)=(cottheta-1)/(cottheta+1)$ ?

Question

21320 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-10-05T18:15:15

see below

$(1-tan theta)/(1+tan theta) = (cot theta -1)/(cot theta +1)$

Right Side: $= (cot theta -1)/(cot theta +1)$

$=(1/tan theta -1)/(1/tan theta +1)$

$=((1-tantheta)/tan theta)/((1+tan theta)/tantheta)$

$=(1-tantheta)/tan theta * tan theta/(1+tan theta)$

$=(1-tan theta)/(1+tan theta)$

$=$ Left Side

How do you prove (1-tantheta)/(1+tantheta)=(cottheta-1)/(cottheta+1)(1-tantheta)/(1+tantheta)=(cottheta-1)/(cottheta+1)?