Question #50e6d Trigonometry Trigonometric Identities and Equations Proving Identities 1 Answer Bdub May 4, 2016 see below Explanation: Left Side:#= sin x/(1-cosx) +(1-cosx)/sinx# #=(sinx * sinx+(1-cosx)*(1-cos x))/(sinx(1-cosx))# #=(sin^2 x + 1-2 cos x+cos^2x)/(sinx(1-cosx))# #=(sin^2x+cos^2x+1-2cosx)/(sinx(1-cosx))# #=(1+1-2cosx)/(sinx(1-cosx))# #=(2-2cosx)/(sinx(1-cosx))# #=(2(1-cosx))/(sinx(1-cosx))# #=2 1/sinx# #=2csc x# #=#Right 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 1669 views around the world You can reuse this answer Creative Commons License