How do you verify the identity $\frac{sin x cos y + cos x sin y}{cos x cos y - sin x sin y} = \frac{tan x + tan y}{1 - tan x tan y}$ $(sinxcosy+cosxsiny)/(cosxcosy-sinxsiny)=(tanx+tany)/(1-tanxtany)$ ?

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How do you verify the identity $\frac{sin x cos y + cos x sin y}{cos x cos y - sin x sin y} = \frac{tan x + tan y}{1 - tan x tan y}$ $(sinxcosy+cosxsiny)/(cosxcosy-sinxsiny)=(tanx+tany)/(1-tanxtany)$ ?

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Answer 1 · 2017-02-15T21:27:22

see below

Explanation:

Right Hand Side:

$\frac{tan x + tan y}{1 - tan x tan y} = \frac{\frac{sin x}{cos x} + \frac{sin y}{cos y}}{1 - \frac{sin x}{cos x} \frac{sin y}{cos y}}$ $(tan x+tan y)/(1-tanxtany)=(sinx/cosx +siny/cosy)/(1-sinx/cosx siny/cosy)$

$= \frac{\frac{sin x cos y + cos x sin y}{cos x cos y}}{1 - \frac{sin x sin y}{cos x cos y}}$ $=((sinxcosy+cosx sin y)/(cosxcosy))/(1-(sinxsiny)/(cosxcosy)$

$= \frac{\frac{sin x cos y + cos x sin y}{cos x cos y}}{\frac{cos x cos y - sin x sin y}{cos x cos y}}$ $=((sinxcosy+cosx siny)/(cosxcosy))/((cosxcosy-sinxsiny)/(cosxcosy)$

$= \frac{sin x cos y + cos x sin y}{cos x cos y} \cdot \frac{cos x cos y}{cos x cos y - sin x sin y}$ $=(sinxcosy+cosxsiny)/(cosxcosy) *(cosxcosy)/(cosxcosy-sinxsiny)$

$=(sinxcosy+cosx sin y)/cancel(cosxcosy) *cancel(cosxcosy)/(cosxcosy-sinxsiny)$

$=(sinxcosy+cosxsiny)/(cosxcosy-sinxsiny)$

$:.=$ Left Hand Side

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How do you verify the identity $\frac{sin x cos y + cos x sin y}{cos x cos y - sin x sin y} = \frac{tan x + tan y}{1 - tan x tan y}$ $(sinxcosy+cosxsiny)/(cosxcosy-sinxsiny)=(tanx+tany)/(1-tanxtany)$ ?

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Explanation:

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Explanation:

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How do you verify the identity $\frac{sin x cos y + cos x sin y}{cos x cos y - sin x sin y} = \frac{tan x + tan y}{1 - tan x tan y}$ $(sinxcosy+cosxsiny)/(cosxcosy-sinxsiny)=(tanx+tany)/(1-tanxtany)$ ?