Question

cos 3A=4 cos^3 A-3 cos A
how to prove it?

Answer 1

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

Answer 2

You can also start like this
cos (3A)

= cos(A + 2A)

Answer 3

I believe you know this identity

Answer 4

yeah i know.. anyway thanks. u r genius man