Simplifying Trigonometric Expressions

Date: 9/13/95 at 4:56:22
From: Tony Snell
Subject: trig. functions

G'day

I was just wondering how you could simplify this expression:

secA.tanA  /   sinA
---------     -----------
1 - cos^2     1-sin^2

those two fractions are being divided.

and I was also wondering how to prove this equation

cosecA.cosec(pi/2 - A).tan(pi - A)=1+tan^2A

Thanks, Tony Snell

Date: 9/16/95 at 15:24:50
From: Doctor Ken
Subject: Re: trig. functions

Hello!

I've got a question about that first expression: are we supposed to divide
the two fractions?  I couldn't quite tell from the way you wrote it.  In 
any case, the first thing you probably want to do is change the 1-Cos^2 A 
to Sin^2 A, and the 1-Sin^2 A to Cos^2 A.  That will certainly make things 
easier.  Also, you can change the SecA TanA to SinA/Cos^2 A.  From there
on, it should just be collecting and cancelling.

In the equation, CscA Csc(Pi/2 - A) is 1/(SinA Sin(Pi/2 - A)).  Since 
Sin(Pi/2 - A) is CosA, this is just 1/(SinA CosA).  Do you see why 
Sin(Pi/2 - A) = CosA?  I'll let you take it from here with this hint.

- Doctor Ken,  The Geometry Forum