Question

Cos ( 3A ) =?..........

Answer 1

Hi here is your answer

Proof: cos 3A
= cos (2A + A)
= cos 2A cos A - sin 2A sin A
= (2 cos^2 A - 1) cos A - 2 sin A cos A ∙ sin A
= 2 cos^3 A - cos A - 2 cos A (1 - cos^2 A)
= 2 cos^3 A - cos A - 2 cos A + 2 cos^3 A
= 4 cos^3 A - 3 cos A
Therefore,  cos 3A = 4 cos^3 A - 3 cos A             Proved

Hope its help you

Answer 2

Cos ( 3A )

= cos(2A + A)
= cos (2A) cos (A) - sin(2A) sin(A)
= [ 2cos^2(A) - 1 ] cos (A) - (2 sin A cos A )sin A
= 2cos^3(A) - cos A - 2sin^2(A) cos A
= 2cos^3(A) - cos A - 2( 1 - cos^2(A)) cos A
= 2cos^3(A) - cos A - 2cos A + 2cos^3(A)
= 4cos^3(A) - 3cos A

Cos ( 3A ) =4cos^3-3cosA