Prove the identity cos(3x)=cos^3(x)-3sin^2(x)cos(x), step by step.

1 answer
Question:

Prove the identity cos(3x)=cos^3(x)-3sin^2(x)cos(x), step by step.

Answers

cos(A+B) = cosAcosB - sinAsinBcos(3x) = cos(x+2x)cos(x+2x)= cosxcos2x-sinxsin2xcos2x = 2cos^2 (x) - 1 sin(2x) = 2sin(x)cos(x)by putting the values we getcos(x+2x)= cosx*cos2x-sinx*sin2x=cosx*(2cos^2 (x) - 1) -(sinx*2sin(x)cos(x))                                                          =cos^3(x)-3sin^2(x)cos(x)hope it helps

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