How do you verify #cos^4 x - sin^4 x = cos^2 x - sin^2 x#? Trigonometry Trigonometric Identities and Equations Proving Identities 1 Answer Kazi Ashiq Iqbal Nov 15, 2015 #cos^4x# - #sin^4x# #(cos^2x)^2 - (sin^2)^2# #(cos^2x+ sin^2x)(cos^2x - sin^2x)# --applying the formula of #a^2 - b^2# # 1 × (cos^2x - sin^2x)# --- since #cos^2x+sin^2x# =1 #cos^2x - sin^2x# 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 1555 views around the world You can reuse this answer Creative Commons License