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Prove that (sin(x+y))/(sin(x-y))=(tanx+t...

Prove that `(sin(x+y))/(sin(x-y))=(tanx+tany)/(tanx-tany)`

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To prove the identity \[ \frac{\sin(x+y)}{\sin(x-y)} = \frac{\tan x + \tan y}{\tan x - \tan y}, \] we will use the sine addition and subtraction formulas, and the definition of tangent. ...
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