If $x+y+z=xyz$, prove that $\frac{2x}{1-x^{2}}+\frac{2y}{1-y^{2}}+\frac{2z}{1-z^{2}}=\frac{2x}{1-x^{2}}\cdot\frac{2y}{1-y^{2}}\cdot\frac{2z}{1-z^{2}}$

Asked Mar 04 '21 at 08:55

Active Mar 04 '21 at 08:55

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How do i proceed with this question? In the book, in solution they have taken $x=\tan A,\ y=\tan B,z=\tan C$. But, isn't it wrong as we have to prove this generally. Please help

asked Mar 04 '21 at 08:55

Soumil Gupta

2

That is generally, as $\tan$ can take any value. – A-Level Student Mar 04 '21 at 09:01
Ok so since, tan and x have the same range, it is a fair assumption right? – Soumil Gupta Mar 04 '21 at 14:27
1

Yes, that's right :-) – A-Level Student Mar 04 '21 at 14:40

If $x+y+z=xyz$, prove that $\frac{2x}{1-x^{2}}+\frac{2y}{1-y^{2}}+\frac{2z}{1-z^{2}}=\frac{2x}{1-x^{2}}\cdot\frac{2y}{1-y^{2}}\cdot\frac{2z}{1-z^{2}}$

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