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