How do you prove #Cos(x+pi/6)-sin(x+pi/6)#? Trigonometry Trigonometric Identities and Equations Proving Identities 1 Answer Bdub Jan 17, 2017 #=sqrt3 /2 cos x - 1/2 sinx - sqrt3 / 2 sinx - 1/2 cos x# Explanation: Use the formulas: #cos(A+B)=cosAcosB-sinAsinB# and #sin(A+B)=sinAcosB+cosAsinB# #cos(x+pi/6)-sin(x+pi/6)=[cosxcos(pi/6)-sinx sin (pi/6)]-[sinx cos(pi/6)+cos x sin (pi/6)]# #=[cosx (sqrt3 /2)-sinx (1/2)]-[sinx (sqrt3 /2)+cos x sin(pi/6)]# #=sqrt3 /2 cos x - 1/2 sinx - sqrt3 / 2 sinx - 1/2 cos 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 2441 views around the world You can reuse this answer Creative Commons License