Prove that $(tanx+tany)/(tanx-tany)=2cscx$ ?

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Answer 1 · 2017-03-26T16:35:05

$(tanx+tany)/(tanx-tany)=-cos(x-y)/cos(x+y)$

not $2cscx$

$(tanx+tany)/(tanx-tany)$

= $(sinx/cosx+cosy/siny)/(sinx/cosx-cosy/siny)$

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

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

= $-cos(x-y)/cos(x+y)$

Hence $(tanx+tany)/(tanx-tany)=-cos(x-y)/cos(x+y)$

not $2cscx$

Prove that (tanx+tany)/(tanx-tany)=2cscx(tanx+tany)/(tanx-tany)=2cscx?