Hi! My teacher told my class that the answer to this question is "1-sin x/cosx" but she wants us to figure out why. I tried solving it but I didn't end up with the answer given. Can someone help me? Thank you!

Question

Problem: cos x/1+sinx

Answer 1

A little "trick" needed here

cosx/(1+sinx) , (those brackets are essential)
= cosx/(1+sinx) * (1-sinx)/(1-sinx) ---> I multiplied by a version of 1, thus changing the appearance but not the value of the expression

= cosx(1-sinx)/(1 - sin^2 x)
= cosx(1-sinx)/cos^2 x
= (1-sinx)/cosx ----- again, I need those brackets.