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Q.

If x+y+z = xyz then  3x-x31-3x2

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a

π3x-x31-3x2

b

π3x+x31-3x2

c

π3x+x31+3x

d

π3x-x31+3x2

answer is A.

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Detailed Solution

x+y+z=xyz

Let  x=tan A, y=tan B, z=tan C

A+B+C=πtan A+tan B+tan C=tan A tan B tan C3A+3B+3C=3πtan3A+tan3B+tan3C=tan3A tan3B tan3Ctan3A=π tan3A3tan A-tan3A1-3tan2A=π 3tan A-tan3A1-3tan2A 3x-x31-3x2=π 3x-x31-3x2

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