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arlik [135]
2 years ago
14

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

Mathematics
1 answer:
earnstyle [38]2 years ago
8 0
Cos(A+B) = cosAcosB - sinAsinB
cos(3x) = cos(x+2x)
cos(x+2x)= cosxcos2x-sinxsin2x
cos2x = 2cos^2 (x) - 1
sin(2x) = 2sin(x)cos(x)
by putting the values we get
cos(x+2x)= cosx*cos2x-sinx*sin2x=cosx*(2cos^2 (x) - 1) -(sinx*2sin(x)cos(x))
                                                          <span>=cos^3(x)-3sin^2(x)cos(x)</span>
hope it helps






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