How do you verify the identity #cot(pi/2-x)=tanx#? Trigonometry Trigonometric Identities and Equations Proving Identities 1 Answer Bdub Feb 6, 2017 see below Explanation: Left Hand Side: #cot(pi/2 -x)=cos(pi/2 -x)/sin(pi/2 -x)# Use the formulas #cos(A-B)=cosAcosB+sinAsinB# and #sin(A-B)=sinAcosB-cosAsinB# #=(cos (pi/2)cosx+sin(pi/2)sinx)/(sin(pi/2)cosx-cos(pi/2)sinx# #=(0*cosx+1*sinx)/(1*cosx-0*sinx)# #=sinx/cosx# #=tanx# #:. = # Right 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 41103 views around the world You can reuse this answer Creative Commons License