Verify this is an identity? cos 3t=cos^3 t-3sin² t cos t

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Answer 1 · 2018-04-03T04:15:59

Verified below

Using:
$cos(x+y)= cosxcosy-sinxsiny$
$sin2x= 2sinxcosx$
$cos2x= cos^2x-sin^2x= 2cos^2x-1= 1-2sin^2x$

$cos 3t=cos^3 t-3sin² t cos t$

$cos(t+2t)=cos^3 t-3sin² t cos t$

$costcos2t-sintsin2t=cos^3 t-3sin² t cos t$

$costcos2t-sint(2sintcost)=cos^3 t-3sin² t cos t$

$cost(cos^2t-sin^2t)-2sin^2tcost=cos^3 t-3sin² t cos t$

$cos^3t-sin^2tcost-2sin^2tcost=cos^3 t-3sin² t cos t$

$cos^3t-3sin^2tcost=cos^3 t-3sin² t cos t$