Question

4 COSA.cos(120+ A) Cos (120-A) = COS3A​

Answer 1

Step-by-step explanation:

4 COSA.cos(120+ A) Cos (120-A)

=2COSA. 2cos(120+ A) Cos (120-A)

=2COSA.(cos(120+ A+120-A) +Cos( (120+A-(120-A)))

=2cosA((cos(240)+cos2A)

=2cosA(cos(180+60)+cos2A)

=2cosA(-cos60+cos2A)

=2cosA(-1/2+cos2A)

= -cosA+2cosAcos2A

= -cosA+cos(A+2A)+cos(A-2A)

= - cosA+cos3A+cos(-A)

= -cosA+cos3A+ cosA (since cos(-A)= cos(A))

=cos3A