I'm trying to see if the teacher didn't give us the right problem or if I'm just not getting it. The problem is "re-write the expression without a fraction: 4/(1-sin x)". I can do it if the problem is sin squared x but I don't know how to solve the problem given. Pls help. thx

Answer 1

multiply by (1+sinx)/(1+sinx) which is really 1, so you are not changing the value, only the appearance.

4/(1-sin x)[(1+sinx)/(1+sinx)] to get
4(1+sinx)/(1 - sin^2 x)
= 4(1+sinx)/cos^2 x
= 4(sec^2 x)(1 + sinx)