How do you prove #-sin( pi/3) = cos ((5pi)/6)#? Trigonometry Trigonometric Identities and Equations Proving Identities 1 Answer A. S. Adikesavan Apr 4, 2016 #-sin(pi/3) = sin (pi+pi/3)= cos (pi/2-(pi+pi/3))=cos(-5pi/6)=cos(5pi/6)# Explanation: #-sinx=sin (pi-x)==cos(pi/2-(pi-x))=cos(-(x+pi/2))=cos(x+pi/2)# Here, #x=pi/3#. 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 1995 views around the world You can reuse this answer Creative Commons License