How do you simplify #2 sin 35 cos 35#? Trigonometry Trigonometric Identities and Equations Double Angle Identities 1 Answer George C. May 12, 2015 Use #e^(i theta) = cos theta + i sin theta# #cos 2theta + i sin 2theta# #= e^(2 i theta)# #= e^(i theta)e^(i theta)# #= (cos theta + i sin theta)(cos theta + i sin theta)# #= (cos^2 theta - sin^2 theta) + i (2 cos theta sin theta)# Looking at the coefficients of #i#, we get #sin (2 theta) = 2 cos theta sin theta = 2 sin theta cos theta# So #2 sin 35^o cos 35^o = sin ( 2*35^o ) = sin 70^o# 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 6369 views around the world You can reuse this answer Creative Commons License