Asked by Ribie
Verify the following identities,
cos 3x = 4 cos^(3) x - 3 cos x
cos 3x = 4 cos^(3) x - 3 cos x
Answers
Answered by
Reiny
LS = cos(3x)
= cos(2x+x)
= cos(2x)cosx - sin(2x)sinx
= (2cos^2 x - 1)(cosx) - 2sinxcosxsinx
= 2cos^3 x - cosx - 2(sin^2x)cosx
= 2cos^3 x - cosx - 2(1 - cos^2 x)cosx
= 2cos^3 x - cosx - 2cosx + 2cos^3 x
= 4cos^3 x - 3cosx
= RS
= cos(2x+x)
= cos(2x)cosx - sin(2x)sinx
= (2cos^2 x - 1)(cosx) - 2sinxcosxsinx
= 2cos^3 x - cosx - 2(sin^2x)cosx
= 2cos^3 x - cosx - 2(1 - cos^2 x)cosx
= 2cos^3 x - cosx - 2cosx + 2cos^3 x
= 4cos^3 x - 3cosx
= RS
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