If the line x = y = z intersects the line x sin A + y sin B + z sin C – 18 = 0 = x sin 2A + y sin 2B + z sin 2C -9, where A, B, C are the angles of a triangle ABC, then 80 
is equal to _______
Text Solution
Verified by Experts5
(5)
Given.
The line x = y = z intersects the line x tin A +y sinB + 2 sinC -18 = 0 = x sin2A + y sin2B + zsin2C=9
So, let x = y= z =k
k(sinA + sinB + sinC)= 18
Now we know that, if A, B & C are angles of triangle then
.....(i)
Also k(sin 2A + sin 2A + sin 2A) = 9
And similarly sin2A+sin2A+sin2A=4sinA.sinB.sinC
........(ii)
Now dividing equation (i) & (ii) we get,
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