How do you simplify #f(theta)=csc4theta-2cot2theta+5sec2theta# to trigonometric functions of a unit #theta#? Trigonometry Trigonometric Identities and Equations Double Angle Identities 1 Answer P dilip_k Nov 21, 2016 #f(theta)=csc4theta-2cot2theta+5sec2theta# #=1/(sin4theta)-(2cos2theta)/(sin2theta)+5/(cos2theta)# #=1/(2sin2thetacos2theta)-(2cos2theta)/(sin2theta)+5/(cos2theta)# #=(1-4cos^2 2theta+10sin2theta)/(2sin2thetacos2theta)# #=(1-4(2cos^2 theta-1)^2+20sinthetacostheta)/(4sinthetacostheta(2cos^2theta-1))# 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 1269 views around the world You can reuse this answer Creative Commons License