How do you verify #sin^4x-cos^4x=1-2cos^2x#? Trigonometry Trigonometric Identities and Equations Proving Identities 1 Answer Bdub Mar 8, 2018 See Below Explanation: #LHS:# #sin^4 x -cos^4 x =(sin^2x-cos^2x) (sin^2x+cos^2x)#->factor #=(sin^2x-cos^2x)*1# #=(1-cos^2x)-cos^2x#->use the property #sin^2x+cos^2x=1# #=1-2cos^2x# #=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 72464 views around the world You can reuse this answer Creative Commons License