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Asked by sarveshvibrantacademy | 21 Mar, 2019, 15:45: PM
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maximum value of cos-1(x) = π .
 
Hence if cos-1(a) + cos-1(b) + cos-1(c) = 3π, then cos-1(a) = cos-1(b) = cos-1(c) = π
 
hence a = b = c = -1 .............................(1)
 
Given f(1) = 2 and f(x+y) = f(x) f(y) for all x,y
 
f(2) = f(1+1)  = f(1) f(1) = 2×2 = 4
 
f(3) = f(1+2) = f(1) f(2) = 2×4 = 8
 
a2f(1) + b2f(2) + c2f(3) +[ (a+b+c) / ( a2f(1) + b2f(2) + c2f(3) ) ] =  a4 + b8 + c16 + [ (a+b+c) / ( a4 + b8 + c16  ) ] ..................(2)
 
substituting values of a, b and c from (1) in eqn.(2), we get,   1+1+1+[  (-3) / (1+1+1) ] = 2
Answered by Thiyagarajan K | 21 Mar, 2019, 17:51: PM

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