I cannot figure this out to save my life…the answer in the back of my textbook says it simplifies to tanx but I just can’t figure out how to get to that…
Please help!
4 Answers

I’m not 100% sure but this is what i get.
secxcosx/sinx
=1/cosx – cosx / sinx (because secx = 1/cosx)
= 1cos^2x/cosx / sinx (when u obtain a common denominator)
=sin^2x/cosxsinx (because 1cos^2 = sin^x and therefore u can cancel out the square of sin^2x with sinx)
=sinx/cosx
=tanx
hope this helped 🙂

sec x = 1/cos x
Take the numerator : sec x – cos x = 1/cos x – cos x
= ( 1cos ^2 x)/cos x
= sin^2 x/cos x
divide by sin x to get sinx/cosx = tan x

sec = 1/cos.
So, eqn bcom,
((1/cosx)cosx)/sinx.
Cross multiply the numerator. So,
(1cos^2(x))/cosx.sinx
1cos^2(x)=sin^2(x).
Simplify the rest..

We know sec x = 1 / cos x. So then we have
([1 / cos x] – cos x) / sin x
= (1 – cos^2 x) / sin x cos x (multiplying numerator & denominator by cos x)
= sin^2 x / sin x cos x
= sin x / cos x
= tan x