How do you prove #Cotx = -tan(x - pi/2)#? Trigonometry Trigonometric Identities and Equations Proving Identities 1 Answer Bdub May 9, 2016 see below Explanation: Right Side:#=-tan(x-pi/2)# #=-sin(x-pi/2)/cos(x-pi/2)# #=(-sinx cos(pi/2)-cos x sin (pi/2))/((cosxcos(pi/2))+sinx sin (pi/2))# #=-(sinx xx 0-cosx xx 1)/(cos x xx 0+sinx xx 1)# #=-(-cosx/sinx)# #=cot x# 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 2949 views around the world You can reuse this answer Creative Commons License