Simplifying Trigonometric ExpressionsDate: 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 |
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