How would I prove this trig identity:

(1+cos^2x-2cosx)/sin^2x=(1-cosx)/(1+cosx)

Question

How would I prove this trig identity:

(1+cos^2x-2cosx)/sin^2x=(1-cosx)/(1+cosx)

anonymous · Answer

See attached file for a clear version

jdoe0001 · Answer

hmm what "solve" stand for?

anonymous · Answer

Sorry I meant "prove"

jdoe0001 · Answer

wel.. let's take a peek at the left-hand-side
notice the numerator.. can you factor it?

anonymous · Answer

That's what I'm stuck on, I don't get how I can factor the numerator.

jdoe0001 · Answer

ok... let us take a closer look at  it
$\bf \cfrac{1+cos^2(x)-2cos(x)}{sin^2(x)}=\cfrac{1-cos(x)}{1+cos(x)}
\ \quad \
1+cos^2(x)-2cos(x)\implies cos^2(x)-2cos(x)+1
\ \quad \\
 [{\color{brown}{ cos(x)}}]^2-2{\color{brown}{ cos(x)}}+1\implies (\square ?-\square ?)(\square ?-\square ?)$

jdoe0001 · Answer

notice, the numerator of the left-side is just a quadratic equation, thus you could just factor it like any quadratic one