I need help with a proof please?

Question

SecX - 1 / TanX = TanX / 1 + SecX

Been working on this for about an hour and can't get a resolution.  Any thoughts?

nyc_kid · Accepted Answer

I assume you meant: (SecX - 1) / TanX = TanX / (1 + SecX). If so, proceed:to prove that:
 (SecX - 1)(1 + SecX) = (TanX )^2
But (SecX - 1)1 + SecX)  = (SecX)^2 - 1 = (1/CosX)^2 - 1 = (1-(CosX)^2)/(CosX)^2 = (SinX)^2/(CosX)^2) = (TanX)^2
!

Johnny · Answer

Could you use parenthesis, to better help understand which part is in the numerator and denominator.

Your questions could be:

(secx - 1) / tanx = tanx / (1 + secx)

or 

secx - (1 / tanx) = (tanx / 1) + secx

Thanks!

? · Answer

You have...

sec=1/cos
tan=sin/cos
1/tan=cos/sin

So, I'd multiply the equation by cosX to get it to...

1 - cos^2(X)/sinX = sinX + 1

Multiplying by sinX gives...

sinX - cos^2(X) = sin^2(X) + sinX

Which boils down to...

0 = sin^2(X) + cos^2(X) = 1 and the universe implodes.

? · Answer

Check this link out.

I need help with a proof please?

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