How do you prove #(1 + csc A)(1 - sin A) = cotA cosA#? Trigonometry Trigonometric Identities and Equations Proving Identities 1 Answer Alan P. May 2, 2015 Remember that #csc(A) = 1/sin(a)# and #cot(A) = cos(A)/sin(A)# Therefore #1+csc(A))(1-sin(A))# #=1+1/sin(A)-sin(A)-sin(A)/sin(A)# #=(1-sin^2(A))/sin(A)# #=cos^2(A)/sin(A)# #= cos(A)/sin(A) * cos(A)# #=cot(A)*cos(A)# 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 3462 views around the world You can reuse this answer Creative Commons License