SOLUTION: Given cot u=2/5 and cos v=-3/5 find tan(u+v) assume 0<u<pi/2 and pi<v<3pi/2

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Question 847656: Given cot u=2/5 and cos v=-3/5 find tan(u+v)
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Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
Given cot u=2/5 and cos v=-3/5 find tan(u+v)
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Identity: tan(u+v)=(tanu+tanv)/(1-tanu*tanv)
cotu=3/5
tanu=5/3
..
in Q2
cosv=-3/5
sinv=4/5
tanv=sin/cos=-4/3
..
tan(u+v)=(5/3+(-4/3))/(1-5/3*(-4/3))=(1/3)/(1+(20/9)=(1/3)/(29/9)=3/29
calculator check:
tanu=5/3
u≈59.04˚
cosv=-3/5 (in Q2)
v≈126.87
(u+v)≈185.91˚
tan(u+v)=tan(185.91)≈0.1034
exact value=3/29≈0.1034