Question

If a, b, c are the sides of a triangle then the range of
a2+b2+C2/ab + bc+ ca

Answer 1

Answer:

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Step-by-step explanation:

Correct option is

B

(21,1]

For a trianglesinAa=sinBb=sinCc

Therefore

a=sinCc(sinA) and b=sinCc(sinB)

By substituting we get the above expression as

sin2A+sin2B+sin2CsinAsinB+sinBsinC+sinCsinA

Multiplying and dividing by 2 we get

2(sin2A+sin2B+sin2C)2(sinAsinB+sinBsinC+sinCsinA)

=21[sin2A+sin2B+sin2C(sinA+sinB+sinC)2−(sin2A+sin2B+sin2C)]

=21[