How do you prove #sin( (3π/2) + x ) + sin ( (3π/2) - x ) = - 2 cos x#? Trigonometry Trigonometric Identities and Equations Double Angle Identities 1 Answer A. S. Adikesavan Mar 21, 2016 Use #sin(A+B)+sin(A-B) = 2 sin A cos B#. Explanation: Here, A = #3pi/2# and B = x. #sin(3pi/2) = sin (pi+pi/2)=-sin(pi/2)=-1.# Answer link Related questions What are Double Angle Identities? How do you use a double angle identity to find the exact value of each expression? How do you use a double-angle identity to find the exact value of sin 120°? How do you use double angle identities to solve equations? How do you find all solutions for #sin 2x = cos x# for the interval #[0,2pi]#? How do you find all solutions for #4sinthetacostheta=sqrt(3)# for the interval #[0,2pi]#? How do you simplify #cosx(2sinx + cosx)-sin^2x#? If #tan x = 0.3#, then how do you find tan 2x? If #sin x= 5/3#, what is the sin 2x equal to? How do you prove #cos2A = 2cos^2 A - 1#? See all questions in Double Angle Identities Impact of this question 4562 views around the world You can reuse this answer Creative Commons License