If #costheta=-15/17# and #pi/2<theta<pi#, how do you find #cos2theta#? Trigonometry Trigonometric Identities and Equations Double Angle Identities 1 Answer Gerardina C. Nov 12, 2016 #161/289# Explanation: Since #cos2theta=cos^2theta-sin^2theta# and #sin^2theta=1-cos^2theta#, you will have: #cos2theta=cos^2theta-(1-cos^2theta)=2cos^2theta-1# #=2(-15/17)^2-1# #=2*225/289-1# #=(450-289)/289=161/289# 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 5520 views around the world You can reuse this answer Creative Commons License