Trigonometry ProofDate: 7/18/96 at 4:32:59 From: Anonymous Subject: Trig. Proof I would appreciate any help that you may be able to give. (cotX)(cosX) cosX -------------- = ------- (cotX) + (cosX) 1+ sinX I have to prove this question, not answer or solve. Thank you in advance. Date: 7/18/96 at 13:1:55 From: Doctor Paul Subject: Re: Trig. Proof Here's how to prove both sides of your equation are equal: cot(x) * cos(x) cos(x) --------------- = --------- cot(x) + cos(x) 1 + sin(x) I really didn't know where to begin. There is usually some sort of substitution to make in these trig identity problems (like (sin(x))^2 = 1 - (cos(x))^2) but there weren't any obvious substitutions here. I began by cross multiplying: [cot(x)*cos(x)]+[cot(x)*cos(x)*sin(x)] = [cot(x)*cos(x)] + [(cos(x)* cos(x)] Recall that tan(x) is really sin(x) / cos(x) and that cot(x) is the 1 / tan(x), so cot(x) = cos(x) / sin(x). Let's make that substitution: [cos(x)*cos(x)] [cos(x)*cos(x)*sin(x)] ------------- + --------------------- = sin(x) sin(x) [cos(x)*cos(x)] [(cos(x)*cos(x)] ------------- + ------------- sin(x) 1 I don't think it's too hard to see the two sides are equal..just cancel the two sin(x) terms in the second of the four brackets and you're in business.. -Doctor Paul, The Math Forum Check out our web site! http://mathforum.org/dr.math/ Date: 7/18/96 at 15:59:8 From: Doctor Anthony Subject: Re: Trig. Proof >prove (cot x * cos x)/(cot x + cos x) = (cos x)/(1 + sin x) These questions are easily answered if you remember the relationships between the various trig. ratios. In this case use cot(x) = cos(x)/sin(x) So the lefthand side of the above expression can be written: [cos(x)/sin(x)]*cos(x) ---------------------- cos(x)/sin(x) + cos (x) Multiplying the top and bottom by sin(x), we get cos(x)*cos(x) --------------------- cos(x) + sin(x)*cos(x) Dividing the top and bottom by cos(x) and we get: cos(x) --------- = righthand side. 1 + sin(x) -Doctor Anthony, The Math Forum Check out our web site! http://mathforum.org/dr.math/ |
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