How do you simplify using the double angle formula #cos^2(-105)-sin^2(-105)#? Trigonometry Trigonometric Identities and Equations Double Angle Identities 1 Answer Ratnaker Mehta Sep 15, 2016 #-sqrt 3/2.# Explanation: Recall that #(1) : cos 2theta=cos^2 theta-sin^2 theta.# #(2) : cos (-theta)=cos theta, &, (3) : cos (180+theta)=-cos theta.# Here, #theta = -105", so the expression = "cos(2*(-105))# #=cos (-210)=cos (210) =cos (180+30)=-cos 30=-sqrt 3/2.# 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 9298 views around the world You can reuse this answer Creative Commons License