How do you simplify #-sin4theta-cos2theta+sin^2theta# to trigonometric functions of a unit #theta#? Trigonometry Trigonometric Identities and Equations Double Angle Identities 1 Answer Konstantinos Michailidis Dec 26, 2015 We have that #sin(4theta)=2sin(2theta)*cos(2theta)=2*sin(theta)*cos(theta)(cos^2(theta)-sin^2(theta))# #cos(2theta)=cos^2(theta)-sin^2(theta)# Hence #-sin(4theta)-cos(2theta)+sin^2(theta)=-2*sin(theta)*cos(theta)(cos^2(theta)-sin^2(theta))-(cos^2(theta)-sin^2(theta))+sin^2theta# 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 1973 views around the world You can reuse this answer Creative Commons License