Question

How do I do these questions? I'm supposed to prove them so that both sides are the same and I'm only supposed to manipulate one side and leave the other side alone but I'm stuck.

Problem 1. (secx/cosx)-(cscx/sinx)=tan^2x-cot^2x


Problem 2. secx+cscx=(1+tanx)/sinx

Answer 1

1.

LS = (1/cosx) / cosx - (1/sinx) /sinx
= 1/cos^2 x - 1/(sin^2 x)
= (sin^2x + cos^2x)/cos^2x - (sin^2x + cos^2x)/sin^2x
= sin^2x/cos^2x + cos^2x/cos^2x - sin^2x/sin^2x - cos^2x/sin^2x
= tan^2x + 1 - 1 - cot^2x
= tan^2x - cot^2x
= RS

2. RS = (1+tanx)/sinx
= 1/sinx + tanx/sinx
= cscx + (sinx/cosx) /sinx
= cscx + 1/cosx
= cscx + secx
= LS