How do you verify the identity #sin4x= 4sinxcosx(1-sin^2x)#? Trigonometry Trigonometric Identities and Equations Proving Identities 1 Answer Alan P. Apr 23, 2015 Remember #sin(2theta) = 2*sin(theta)*cos(theta)# and #cos(2theta) = 1 - 2*sin^2(theta)# So #sin(4x)# #= 2*sin(2x)*cos(2x)# #=2 * (2 * sin(x) * cos(x) )* (1-2 * sin^2(x))# #=4sin(x)cos(x)(1-sin^2(x))# 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 13995 views around the world You can reuse this answer Creative Commons License