(a) Prove that cos 3A = 4cos³ A - 3 cos A

GodLesZ asked Mar 21, 2022

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GodLesZ asked Mar 21, 2022

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10 votes

Answer:

Explanation:

cos 3A = cos (2A+A)

= cos 2A cos A - sin 2A sin A

= (2cos
A^(2) -1) cos A - (2sinAcosA) sinA

=2cos
A^(3) -cosA - 2sin
A^(2) cosA

=2cos
A^(3) -cosA -2(1 -cos
A^(2) )cosA

=2cos
A^(3) - cosA - 2 cosA+ 2cos

⇒ ∴4cos
A^(3) -3 cosA

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