Homework Help: Pre-Cal

Posted by Alycia on Thursday, November 1, 2012 at 4:19pm.

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

Pre-Cal - Reiny, Thursday, November 1, 2012 at 5:55pm
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

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