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

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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

Explanation:

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

$cos 3t=cos^3 t-3sin² t cos t$

$cos(t+2t)=cos^3 t-3sin² t cos t$

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

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

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

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

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

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

1 Answer

Explanation:

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