Question

Aratati ca r este numar rational
r=sin 36°/sin 12°-cos36°/cos12°

Answer 1

Ne vom folosi de urmatoarele 2 formule
$\sin{(a-b)}=\sin{a}\cos{b}-\sin{b}\cos{a}$
$\sin{2a}=2\sin{a}\cos{a}$
Atunci
$r=\frac{\sin{36}}{\sin{12}}-\frac{\cos{36}}{\sin{12}}=\frac{\sin{36}\cos{12}-\sin{12}\cos{36}}{\sin{12}\cos{12}}=\frac{\sin{(36-12)}}{\frac{\sin{2*12}}{2}}=2*\frac{\sin{24}}{\sin{24}}=2$