SOLUTION: I am working on homework and can't figure out how to do this problem.
Write sin(cot^-1(u)+ cot^-1(v)) as an algebraic expression containing u and v
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Write sin(cot^-1(u)+ cot^-1(v)) as an algebraic expression containing u and v
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Question 678349: I am working on homework and can't figure out how to do this problem.
Write sin(cot^-1(u)+ cot^-1(v)) as an algebraic expression containing u and v Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website! Write sin(cot^-1(u)+ cot^-1(v)) as an algebraic expression containing u and v
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Because you want the sin of a sum you need the sin and the cos
of the angles involved.
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If the cot is u/1 find the sin and the cos
sin = 1/sqrt(u^2+1) ; cos = u/sqrt(u^2+1)
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If cot is v/1.
sin = 1/sqrt(v^2+1) ; cos = v/sqrt(v^2+1)
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Back to Your Problem:
sin(cot^-1(u)+ cot^-1(v))
= sin[cot^-1(u)]*cos[cot^-1(v)]
+ [u/sqrt(u^2+1)]
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The denominators are the same.
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= [v + u]/[sqrt[(u^2+1)(v^2+1)]
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Cheers,
Stan H.
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