Question

لی
9. If cos (a – B) + cos (B – y) + cos (y – a) =
3/2
prove that ;
cos a + cos ß + cos y = sin a + sin ß + sin y = 0.​

Answer 1

Step-by-step explanation:

cos(a - b) +cos(b-c) + cos(c - a) =-3/2

2(cosacosb + sinasinb+cosbcosc+sinbsinc + cosccosa + sincsina) = -3

2(cosacosb + sinasinb+ cosbcosc + sinbsinc + cosccosa + sincsina) = (1+1+1)

2cosacosb+ 2sinasinb + 2cosbcosc + 2sinbsinc + 2cosccosa + 2sincsina = (sin^2a + cos^2a) - (sin^2b+ cos^2b) (sin^2c + cos^2c)

2cos^2a + cos^2b + cos^2c +2cosacosb+2cosbcosc+ 2cosccosa + (sin^2a + sinb + sin^2c +2sinasinb + 2sinbsinc +2sincsina) = 0

(cosa+cosb + cosc)^2 + (sine + sinb + sinc)^2 = 0 cosa + cosb + coSC = 0, sina + sinb + sinc = 0 Cosa + cosb+ cosc = sina+ sinb + sinc =0

Answer 2

sorry for bad handwriting but i hope it will help