How do you prove Cotx = -tan(x - pi/2)cotx=−tan(x−π2)? Trigonometry Trigonometric Identities and Equations Proving Identities 1 Answer Bdub May 9, 2016 see below Explanation: Right Side:=-tan(x-pi/2)=−tan(x−π2) =-sin(x-pi/2)/cos(x-pi/2)=−sin(x−π2)cos(x−π2) =(-sinx cos(pi/2)-cos x sin (pi/2))/((cosxcos(pi/2))+sinx sin (pi/2))=−sinxcos(π2)−cosxsin(π2)(cosxcos(π2))+sinxsin(π2) =-(sinx xx 0-cosx xx 1)/(cos x xx 0+sinx xx 1)=−sinx×0−cosx×1cosx×0+sinx×1 =-(-cosx/sinx)=−(−cosxsinx) =cot x=cotx Answer link Related questions What does it mean to prove a trigonometric identity? How do you prove \csc \theta \times \tan \theta = \sec \thetacscθ×tanθ=secθ? How do you prove (1-\cos^2 x)(1+\cot^2 x) = 1(1−cos2x)(1+cot2x)=1? How do you show that 2 \sin x \cos x = \sin 2x2sinxcosx=sin2x? is true for (5pi)/65π6? How do you prove that sec xcot x = csc xsecxcotx=cscx? How do you prove that cos 2x(1 + tan 2x) = 1cos2x(1+tan2x)=1? How do you prove that (2sinx)/[secx(cos4x-sin4x)]=tan2x2sinxsecx(cos4x−sin4x)=tan2x? How do you verify the identity: -cotx =(sin3x+sinx)/(cos3x-cosx)−cotx=sin3x+sinxcos3x−cosx? How do you prove that (tanx+cosx)/(1+sinx)=secxtanx+cosx1+sinx=secx? How do you prove the identity (sinx - cosx)/(sinx + cosx) = (2sin^2x-1)/(1+2sinxcosx)sinx−cosxsinx+cosx=2sin2x−11+2sinxcosx? See all questions in Proving Identities Impact of this question 2987 views around the world You can reuse this answer Creative Commons License