Prove it please. ?

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1 Answer
Apr 1, 2018

#64cos^3thetasin^4theta=cos7theta-cos5theta-3cos3theta+3costheta#

Explanation:

#64cos^3thetasin^4theta#

= #8cos^3thetasin^3theta*8sintheta#

= #(sin2theta)^3*8sintheta#

= #2*2sin2thetasintheta*2sin^2 2theta#

= #2*(cos(2theta-theta)-cos(2theta+theta))*(1-cos4theta)#

= #2*(costheta-cos3theta)*(1-cos4theta)#

= #2costheta-2cos3theta-2costhetacos4theta+2cos4thetacos3theta#

= #2costheta-2cos3theta-(cos5theta+cos3theta)+(cos7theta+costheta)#

= #cos7theta-cos5theta-3cos3theta+3costheta#