If x+y+z=xyz, find \frac{3x-x^3}{1-3x^2}+\frac{3y-y^3}{1-3y^2}+\frac{3z-z^2}{1-3z^2}

Dania Robbins

Dania Robbins

Answered question

2022-04-28

If x+y+z=xyz, find 3xx313x2+3yy313y2+3zz213z2

Answer & Explanation

impire7vw

impire7vw

Beginner2022-04-29Added 19 answers

We can not make A+B+C=π
as tan(A+B+C)=tanAtanAtanBtanC1tanAtanB
tanA=tanAtanBtanCtan(A+B+C) where n is any integer [Clearly, you have taken a special value of n]
Now for any integer m,m(A+B+C)=mnπtan(mA+mB+mC)
=tanmnπ=0
tanmA=tanmAtanmBtanmC
Now set m=3 and apply tan3x formula

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