Prove that Cos3A = 4cos^3A - 3cosA ?
ANSWER)
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