Given tantheta=5/12 and pi<theta<(3pi)/2, how do you find cos2theta? Trigonometry Trigonometric Identities and Equations Double Angle Identities 1 Answer Alberto P. Oct 28, 2016 cos2theta=119/169 Explanation: Parametric formula for cosalpha cosalpha=(1-t^2)/(1+t^2) where t=tan(alpha/2) 2theta=alpha, theta=alpha/2 cos2theta=(1-(5/12)^2)/(1+(5/12)^2)=119/169 5/12 < 1\ \ \ so \ \ \ pi < theta < 5/4pi 2pi < 2theta <5/2pi 0 < cos2theta < 1 119/169 is acceptable 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 10632 views around the world You can reuse this answer Creative Commons License