How do you prove #(sinx - tanx)(cosx - cotx) = (sinx -1)(cosx -1)#? Trigonometry Trigonometric Identities and Equations Proving Identities 2 Answers Sahar Mulla ❤ Apr 3, 2018 #L.H.S = (sinx−tanx)(cosx−cotx)# #=> (sinx−sinx/cosx)(cosx−cosx/sinx)# #=> ((sinxcosx−sinx)/cosx)((cosxsinx−cosx)/sinx)# #=> 1/(cosxsinx)(sinxcosx−sinx)(cosxsinx−cosx)# #=> 1/(cosxsinx)(sin^2xcos^2x-cos^2xsinx-sin^2xcosx+sinxcosx)# #=> (sinxcosx-cosx-sinx+1)# #=> cosx(sinx-1) -1(sinx-1)# #=>( cosx-1)(sinx-1)# Answer link P dilip_k Apr 3, 2018 #L.H.S = (sinx−tanx)(cosx−cotx)# #=tanx (sinx/tanx−tanx/tanx)*cotx(cosx/cotx−cotx/cotx)# #=tanx*cotx (sinx/(sinx/cosx)−1)(cosx/(cosx/sinx)−1)# #=(cosx-1)(sinx-1)=RHS# 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 10958 views around the world You can reuse this answer Creative Commons License