How do you simplify #5sec2theta-csc2theta# to trigonometric functions of a unit #theta#? Trigonometry Trigonometric Identities and Equations Double Angle Identities 1 Answer Shwetank Mauria Apr 5, 2018 #5sec2theta-csc2theta=(10sinthetacostheta-2cos^2theta+1)/(4sinthetacos^3theta-2sinthetacostheta)# Explanation: We can use #sin2theta=2sinthetacostheta# and #cos2theta=2cos^2theta-1# Hence #5sec2theta-csc2theta# = #5/(cos2theta)-1/(sin2theta)# = #(5sin2theta-cos2theta)/(sin2thetacos2theta)# = #(10sinthetacostheta-2cos^2theta+1)/(2sinthetacostheta(2cos^2theta-1))# = #(10sinthetacostheta-2cos^2theta+1)/(4sinthetacos^3theta-2sinthetacostheta)# 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 1501 views around the world You can reuse this answer Creative Commons License