Question Number 14592 by Tinkutara last updated on 02/Jun/17
Commented by mrW1 last updated on 02/Jun/17
$$\mid\mathrm{cos}\:{x}\mid=\frac{{q}}{{p}}\leqslant\mathrm{1} \\ $$$$\mid\mathrm{cos}\:{y}\mid=\frac{{u}}{{v}}\leqslant\mathrm{1} \\ $$$$\mid\mathrm{cos}\:{z}\mid=\frac{\mathrm{1}}{\frac{{qu}}{{pv}}}=\frac{{pv}}{{qu}}\geqslant\mathrm{1}\leqslant\mathrm{1} \\ $$$${that}\:{means}\:{the}\:{absolute}\:{value}\:{of} \\ $$$$\mathrm{cos}\:{x},\:\mathrm{cos}\:{y}\:{and}\:\mathrm{cos}\:{z}\:{must}\:{be}\:\mathrm{1}. \\ $$$${there}\:{are}\:\mathrm{4}\:{possibilities}: \\ $$$$\left({x},{y},{z}\right)=\left(\mathrm{0},\mathrm{0},\mathrm{0}\right),\left(\mathrm{0},\pi,\pi\right),\left(\pi,\mathrm{0},\pi\right),\left(\pi,\pi,\mathrm{0}\right) \\ $$
Commented by Tinkutara last updated on 03/Jun/17
$$\mathrm{Thanks}\:\mathrm{Sir}! \\ $$