How to prove the following? #cot^(-1)7+cot^(-1)8+cot^(-1)18=cot^(-1)3# Trigonometry Trigonometric Identities and Equations Proving Identities 1 Answer P dilip_k Mar 1, 2017 #LHS=cot^-1 7+cot^-1 8+cot^-1 18# #=cot^-1 ((7xx8-1)/(8+7))+cot^-1 18# #=cot^-1 (55/15)+cot^-1 18# #=cot^-1 (11/3)+cot^-1 18# #=cot^-1 ((11/3xx18-1)/(11/3+18))# #=cot^-1 ((66-1)/((11+18*3)/3))# #=cot^-1 3=RHS# 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 22912 views around the world You can reuse this answer Creative Commons License