Find the exact value of tan(alpha - beta)

label Calculus
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given cot(alpha) = (2/5), 0<(alpha)<(pi/2) and cos(beta) = (-7/25), (pi)<(beta)<(3pi/2)

Find the exact value of tan(alpha - beta)

Mar 20th, 2015

Because cot(alpha) is in quadrant I, tan is positive, and cos(beta) being in quadrant III, makes tan positive as well.

Thus, tan(alpha-beta) = (tan(alpha)-tan(beta))/(1+tan(alpha)tan(beta))

tan alpha = 1/cot(alpha) = 5/2

tan beta = sqrt(1-cos(beta))/cos(beta) = about 3.428

Therefore, tan(alpha-beta) = -0.097

Mar 20th, 2015

Hey coolartboy,

I could have added a few more steps, but I just ran out of time, so I will now.

First off, I made a mistake in that

tan beta = sqrt(1-cos^2(beta))/cos(beta) = sin(beta)/cos(beta) = sqrt(1-(49/625))/(-7/25)) = sqrt(576/625)/(-7/25) = (24/25)/(-7/25) = 24/7

So, tan(alpha-beta) = -0.097.

Mar 20th, 2015

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