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(tanA+tanB)/(tanA-tanB)=sin(A+B)/(sin(A-...

`(tanA+tanB)/(tanA-tanB)=sin(A+B)/(sin(A-B)`

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LHS:`(tanA+tanB)/(tanA−tanB)`
=`((sinA)/(cosA)+(sinB)/(cosB))/((sinA)/(cosA)−(sinB)/(cosB))`
=`((sinAcosB+cosAsinB)/(cosAcosB))/((sinAcosB+cosAsinB)/(cosAsinB))`
=`(sin(A+B))/(sin(A−B))`
`(tanA+tanB)/(tanA−tanB)=(sin(A+B))/(sin(A−B))`
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