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If a+b=c, prove that cos^2 a+cos^2b+cos^2c =1+2cosacosbcosc

If a+b=c, prove that cos^2 a+cos^2b+cos^2c =1+2cosacosbcosc

Grade:12

1 Answers

Y RAJYALAKSHMI
45 Points
6 years ago
cos^2a +cos^2b+cos^2c= (1+cos2a)/2+(1+cos2b)/2+cos^2c
=1+(1/2)*(2cos(a+b)cos(a-b) +cos^2c   (since a+b+c = 0)
=1 + cos(-c)cos(a-b)+cos^2c          (since cos(-a) = cosa)
=1+cos(c)cos(a-b)+cos^2c
=1+cosc(cos(a-b)+cos(a+b)   (since a+b+c = 0 & cos(-a) = cosa)
=1+cosc(2cosacosb)
=1+2cosacosbcosc
 

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