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

How do you prove cos3theta=4cos^3theta-3costhetacos3theta=4cos^3theta-3costheta?