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x,y,z are respectively the sines and p,q,r are respectively the cosines of angles A,B,C which are in AP with common difference 2pi/3 i.e 120 degrees then prove that the value of 8x 2 (qy – rz) + 8y 2 (rz – px) + 8z 2 (px – qy) is (27) 1/2

x,y,z are respectively the sines and p,q,r are respectively the cosines of angles A,B,C which are in AP with common difference 2pi/3 i.e 120 degrees
then prove that the value of
8x2(qy – rz) + 8y2(rz – px) + 8z2(px – qy) is    (27)1/2

Grade:11

2 Answers

srikar
40 Points
6 years ago
sinA=x  sinB=y    sinc=z
 
put A = 0
 
x=o      y=sin(120)       z=sin(240)
 
8x2(qy – rz)=0
8y2(rz – px) = 8sin2120(sin240cos240)
                   = 4sin2120(sin480)   = 4sin3120  =4(3*31/2)/8   = 3*31/2/2
 
8z2(px – qy) = 8sin2240(-sin120cos120)
                    = 4sin2240(-sin240)  = 4sin360 = 3*31/2/2
 
8x2(qy – rz) + 8y2(rz – px) + 8z2(px – qy) =
    0               +   3*31/2/2       +    3*31/2/2   =  3*31/2 = 271/2
Kaustubh Nayyar
27 Points
6 years ago
can you please do the ques without taking any of the angle by yourself.

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