Question

cos2A + cos2B + cos2C = -1-4cosA cosB cosC
where A + B + C = pi

Answer 1

heya friends.❤

Here is ur answer ..
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From lhs...

cos2A+cos2B+cos2C

=>2cos^2-1+【cos2B+cos2C】【.°.cos2A=cos^2A-1】

=>2cos^2A-1+【2cos(2B+2C)/2*(cos(2B-2C)】【As we know that cosA+cosB=2cos(A+B)/2*cos(A-B)just like that...】

=>2cosA-1+【2cos(B+C)*(cos(B-C)】

=>2cos^2A-1+【2cos(180°-(A)*cos(B-C)..
.*.(A+B+C)=180°

.*.B+C=180-A.....using above line..

so,-1+2cosA(cosA*cos(B-C)

=>-1+2cosA【2cosA*cos(B-C)】

=>-1+2cosA【cosA*cos(B-C)】

=>-2cosA【-cos(B+C)+cos(B-C)

.*.A+B+C=180°
=>A=180°-(B+C) above use.....

=>-1+2cosA【-cos(B+C+B-C)/2*Cos(B+C-B+C)/2

=>-1+2cosA【2cosB*cosC】

=>-1+2cosA【2cosB*Cosc】

=>-1-4cosA*cosB*cosC.prooved...

hope it help you....

@Rajukumar☺☺☺