How do you verify (sinA-cosA)^2=1-2sin^2AcotA? Trigonometry Trigonometric Identities and Equations Proving Identities 1 Answer Bdub Nov 12, 2016 see below Explanation: (sinA-cosA)^2=1-2sin^2AcotA (sinA-cosA)(sinA-cosA)=1-2sin^2A*cosA/sinA sin^2A-2sinAcosA+cos^2A=1-2sin^cancel2AcosA/cancelsinA sin^2A+cos^2A-2sinAcosA=1- 2 sinA cos A 1-2 sin A cos A=1- 2 sinA cos A :.Left Hand Side = Right Hand 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 6236 views around the world You can reuse this answer Creative Commons License