How do you verify #[sin^3(B) + cos^3(B)] / [sin(B) + cos(B)] = 1-sin(B)cos(B)#? Trigonometry Trigonometric Identities and Equations Proving Identities 1 Answer ProfLayton Apr 22, 2016 Proof below Explanation: Expansion of #a^3+b^3=(a+b)(a^2-ab+b^2)#, and we can use this: #(sin^3B+cos^3B)/(sinB+cosB)=((sinB+cosB)(sin^2B-sinBcosB+cos^2B))/(sinB+cosB)# #=sin^2B-sinBcosB+cos^2B# #=sin^2B+cos^2B-sinBcosB# (identity: #sin^2x+cos^2x=1#) #=1-sinBcosB# 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 4764 views around the world You can reuse this answer Creative Commons License