How do you simplify #3cos8theta-6sin4theta# to trigonometric functions of a unit #theta#?

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Answer 1 · 2016-11-25T03:34:36

#=3(2(2(2cos^2theta-1)^2-1)^2-1)-12sin theta cos theta (2 cos^2 theta-1)#

#3 cos 8theta- 6 sin 4theta#

#=3(2 cos^2 4theta-1)-6 sin 2theta cos 2theta#

#=3(2(2 cos^2 2theta-1)^2-1)-12 sin theta cos theta (2cos^2theta-1)#

#=3(2(2(2cos^2theta-1)^2-1)^2-1)-12sin theta cos theta (2 cos^2 theta-1)#

Also, Comparison of real and imaginary parts in

#cos ntheta+i sin ntheta = (cos theta+i sin theta)^n, n = 4 and 8# can

be used as an alternative method. This is good, when m and n are

large, for expressions of the form #a cos mtheta + b sin ntheta)#.