How do you prove #cos3theta=4cos^3theta-3costheta#?

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Answer 1 · 2016-10-05T17:22:29

see below

#cos 3theta = 4 cos^3 theta - 3 cos theta#

Left Side #=cos 3 theta#--> Use #cos (A+B) = cos A cos B -sin A sin B# formula

#cos 3 theta = cos(2theta+theta)=cos 2 theta cos theta -sin 2 theta sin theta#

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

#=2 cos ^3 theta -cos theta-2 cos theta sin ^2 theta#

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

#=2 cos ^3 theta -cos theta-2 cos theta+2 cos^3 theta#

#=4cos^3 theta -3cos theta#

#=#Right Side