How do you simplify #f(theta)=2tan2theta-3sin2theta+csc2theta# to trigonometric functions of a unit #theta#? Trigonometry Trigonometric Identities and Equations Double Angle Identities 1 Answer Nghi N. Mar 1, 2016 #2tan 2t = (4tan t)/(1 - tan^2 t)# #3sin 2t = 6sin t.cos t# #csc 2t = 1/sin (2t) = 1/(2sin t.cos t)# Finally, #f(t) = (4tan t)/(1 - tan^2 t) - 6sin t.cos t + 1/(2sin t.cos t)# 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 1235 views around the world You can reuse this answer Creative Commons License