Mathematics: Prove that cos 3a = cos (2a+a)cos 3a = 4 cos³a – where from the cos a sin a * cos a give cos a? ? cos 3a = cos (2a +a)cos 2a cos a - sin2a sina(2cos²a-1)cosa-(2sina cos a) sina 2cos³a - cos a - 2 sin²a cos a2 cos³a-cos a - 2(1-cos²a)cos a2 cos³a - cos a - 2cos a + 2 cos³acos3a = 4cos³a-3cos a

33 The range is the greatest number (45) minus the least number (12)...

Prove that cos 3a = cos (2a+a)cos 3a = 4 cos³a – where

cnicole71

10.03.2022

Not sure what the question is, but I guess it's to prove that

$\cos3A=4\cos^3A-3\cos A$

Expand the left side as

$\cos3A=\cos(2A+A)=\cos2A\cos A-\sin2A\sin A$

and use the double angle identities to write

$\cos3A=(\cos^2A-\sin^2A)\cos A-2\sin^2A\cos A$

$\cos3A=\cos^3A-3\sin^2A\cos A$

Recall the Pythagorean identity:

$\cos3A=\cos^3A-3(1-\cos^2A)\cos A$

$\cos3A=\cos^3A-3\cos A+3\cos^3A$

$\implies\cos3A=4\cos^3A-3\cos A$

as required.

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