SOLUTION: Angles A and B are acute angles such that tanA + tanB + (tanA)(tanB) = 1 . If A-B = 41 degrees, find the measure of angle A.

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Question 1176723: Angles A and B are acute angles such that tanA + tanB + (tanA)(tanB) = 1 . If A-B = 41 degrees, find the measure of angle A.
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


A student fairly early in his study of trigonometry should recognize the terms in this equation as those in the formula for tangent of the sum of two angles:

tan%28A%2BB%29+=+%28tan%28A%29%2Btan%28B%29%29%2F%281-tan%28A%29%2Atan%28B%29%29

Manipulate the given equation to put it in that form:

tan%28A%29%2Btan%28B%29%2Btan%28A%29%2Atan%28B%29+=+1
tan%28A%29%2Btan%28B%29+=+1-tan%28A%29%2Atan%28B%29
%28tan%28A%29%2Btan%28B%29%29%2F%281-tan%28A%29%2Atan%28B%29%29+=+1
tan%28A%2BB%29+=+1

Since the tangent of 45 degrees is 1, this tells us A+B=45.

But that together with the given that A-B=41 allows us to solve that pair of equations to find the measure of angle A.

I leave that last little bit for you....