x,y,z are respectively the sines and p,q,r are res

Question

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 degreesthen prove that the value of8x2(qy – rz) + 8y2(rz – px) + 8z2(px – qy) is (27)1/2

srikar · Accepted Answer

sinA=x sinB=y sinc=z put A = 0 x=o y=sin(120) z=sin(240) 8x2(qy – rz)=08y2(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

Trigonometry> x,y,z are respectively the sines and p,q,...

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

Kaustubh Nayyar , 10 Years ago

srikar

Kaustubh Nayyar

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Trigonometry> x,y,z are respectively the sines and p,q,...

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 degreesthen prove that the value of8x2(qy – rz) + 8y2(rz – px) + 8z2(px – qy) is (27)1/2

Kaustubh Nayyar , 10 Years ago

srikar

Kaustubh Nayyar

LIVE ONLINE CLASSES

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