Prove that cos 3A = cos (2A+A)

Mathematics

2 answers:

Blababa [14]3 years ago

6 0

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.

olga55 [171]3 years ago

4 0

Answer:

you useless coomstain

Step-by-step explanation:

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You can see also in the picture i post