How do you verify the identity #(tanx+tany)/(1-tanxtany)=(cotx+coty)/(cotxcoty-1)#? Trigonometry Trigonometric Identities and Equations Proving Identities 1 Answer Bdub Apr 19, 2017 see below Explanation: 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 Answer link Related questions What does it mean to prove a trigonometric identity? How do you prove #\csc \theta \times \tan \theta = \sec \theta#? How do you prove #(1-\cos^2 x)(1+\cot^2 x) = 1#? How do you show that #2 \sin x \cos x = \sin 2x#? is true for #(5pi)/6#? How do you prove that #sec xcot x = csc x#? How do you prove that #cos 2x(1 + tan 2x) = 1#? How do you prove that #(2sinx)/[secx(cos4x-sin4x)]=tan2x#? How do you verify the identity: #-cotx =(sin3x+sinx)/(cos3x-cosx)#? How do you prove that #(tanx+cosx)/(1+sinx)=secx#? How do you prove the identity #(sinx - cosx)/(sinx + cosx) = (2sin^2x-1)/(1+2sinxcosx)#? See all questions in Proving Identities Impact of this question 21180 views around the world You can reuse this answer Creative Commons License