Prove the trig identity?
(1+cosx)/(1-cosx) = tan^2x/(sec^2x-1)^2
1 Answer
Jan 14, 2018
Well, let's start from the left...
(1 + cosx)/(1 - cosx)
Multiply through by
= (1 + cosx)/(1 - cosx) cdot (1//cosx)/(1//cosx)
= (1/cosx + 1)/(1/cosx - 1)
Use the fact that
= (secx + 1)/(secx - 1)cdot (secx - 1)/(secx - 1)
= (sec^2x - 1)/(secx - 1)^2
Lastly, use the identity that
= (tan^2x)/(secx - 1)^2
color(red)(ne (tan^2x)/(sec^2x - 1)^2)
And we have shown that the identity is incorrect.