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

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Answer 1 · 2016-06-06T17:18:39

Proof is given below.

#cos3theta=cos(2theta+theta)#

#=cos2thetacostheta-sin2thetasintheta#

#=(cos^2theta-sin^2theta)costheta-2sinthetacosthetasintheta#

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

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

#=costheta(cos^2theta-3sin^2theta)#

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

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

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

#=4cos^3theta-3costheta#