Verify that each equation is an identity Cos3x Cos3 x 3 Si

Verify that each equation is an identity.

Cos(3x) = Cos³ x - 3 Sin² x Cos

Solution

Cos(3x) = Cos3 x - 3 Sin^2 x Cos x

LHS cos(3x) = cos (2x+x)

use the formula cos(a+b) = cosacosb -sinasinb

= cos^3x -sin^2xcosx -2sin^2xcosx

=cos^3x - 3sin^2xcosx