Question #1b8ac Trigonometry Trigonometric Identities and Equations Proving Identities 1 Answer P dilip_k Dec 5, 2016 #(csc x- cot x)(sec x+1)# #=(sinx(csc x- cot x)cosx(sec x+1))/(sinxcosx)# #=((sinxcsc x- sinxcot x)(cosxsec x+cosx))/(sinxcosx)# #=((1- cos x)(1 +cosx))/(sinxcosx)# #=(1- cos^2 x)/(sinxcosx)# #=sin^cancel2 x/(cancelsinxcosx)=sinx/cosx=tanx# 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 1046 views around the world You can reuse this answer Creative Commons License