Question #efcdc Trigonometry Trigonometric Identities and Equations Proving Identities 1 Answer Narad T. Nov 27, 2016 The answer is #=tanx# Explanation: #cscx=1/sinx# #cotx=cosx/sinx# #secx=1/cosx# #cos^2x+sin^2x=1# #tanx=sinx/cosx# #(cscx-cotx)(secx+1)=(1/sinx-cosx/sinx)(1/cosx+1)# #=((1-cosx)/sinx)((1+cosx)/cosx)# #=(1-cos^2x)/(sinxcosx)# #=sin^2x/(sinxcosx)# #=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 1725 views around the world You can reuse this answer Creative Commons License