How do you verify the identity #(tanx+tany)/(1-tanxtany)=(cotx+coty)/(cotxcoty-1)#?

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Answer 1 · 2017-04-19T06:20:13

see below

Right Hand Side:
#color(blue)((cot x+cot y)/(cot xcoty-1)=color(red)((1/tanx + 1/tany)/(1/tanx * 1/tany -1#

#color(red)(=((tany+tanx)/(tanxtany))/((1-tanxtany)/(tanx tany)#

#color(red)(=(tany+tanx)/(tanxtany) *(tanx tany)/ (1-tanxtany)#

#color(red)(=(tany+tanx)/cancel(tanxtany) *cancel(tanx tany)/ (1-tanxtany)#

#color(red)(=(tany+tanx)/ (1-tanxtany)#

#color(red)(=(tanx+tany)/ (1-tanxtany)#

#color(red)(=# Left Hand Side