Question Number 3536 by Syaka last updated on 14/Dec/15
$${prove} \\ $$$$\frac{\mathrm{1}\:+\:{cos}\:{x}\:−\:{cos}\:{y}\:+\:{cos}\:{z}}{\mathrm{1}\:+\:{cos}\:{x}\:+\:{cos}\:{y}\:−\:{cos}\:{z}}\:=\:{cot}\:\frac{\mathrm{1}}{\mathrm{2}}{z}\:.\:{tan}\:\frac{\mathrm{1}}{\mathrm{2}}{y} \\ $$$$ \\ $$
Commented by Yozzii last updated on 14/Dec/15
$${x}={y}=\mathrm{0}\:,\:{z}=\pi/\mathrm{2} \\ $$$$\therefore\:{lhs}=\frac{\mathrm{1}+\mathrm{1}−\mathrm{1}+\mathrm{0}}{\mathrm{1}+\mathrm{1}+\mathrm{1}−\mathrm{0}}=\frac{\mathrm{1}}{\mathrm{3}} \\ $$$${rhs}={cot}\frac{\pi}{\mathrm{4}}{tan}\frac{\mathrm{0}}{\mathrm{2}}=\mathrm{1}×\mathrm{0}=\mathrm{0} \\ $$$${lhs}\neq{rhs}. \\ $$