How do you prove #cos 2x = (1-tan^2x)/(1+tan^2x)#? Trigonometry Trigonometric Identities and Equations Double Angle Identities 1 Answer Nghi N. Jun 8, 2015 Call # tan (x/2) = t # and use the trig identity #cos x = (1 - t^2)/(1 + t^2)#, then #cos 2x = (1 - tan^2 x)/(1 + tan^2 x)# 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 2379 views around the world You can reuse this answer Creative Commons License