Write The Formula For Cos 3A

Answer: Hence, cos3A= −3cosA+4cos3A

First, we find the simplification of the given trigonometry by using the identities cos2A=2cos2A-1 and sin(2A)=2sinAcosA. This brings the value of cos3A down to a more manageable value. We need to express the angle as the sum of two angles so that it is easier to understand.

We already know that cos(X+Y)=cosXcosY-sinAsinB is the identity of the function. In order to find the ultimate solution, we change the values to X=2A, and Y=A.

cos 3A can be written as

cos3A=cos(2A+A)—–(i)

We know the trigonometric identity

cos(a+b)=cos(a)cos(b)-sin(a)sin(b)

Applying the above identity to equation (i) we get,

cos 3A =cos2AcosA−sin2AsinA

=(−1+2cos2A)cosA−2cosAsinAsinA

=−cosA+2cos3A−2sin2AcosA

=−cosA+2cos 3A−2(1−cos2A)cosA

=−3cosA+4cos3A