Question

Calcule o cossec 15?

Answer 1

$cossec15^o=\\\\\frac{1}{\sin15^o}=\\\\\frac{1}{\sin(45^o-30^o)}=\\\\\frac{1}{\sin45^o\cdot\cos30^o-\sin30^o\cdot\cos45^o}=\\\\\frac{1}{\frac{\sqrt{2}}{2}\cdot\frac{\sqrt{3}}{2}-\frac{1}{2}\cdot\frac{\sqrt{2}}{2}}=\\\\\frac{1}{\frac{\sqrt{6}}{4}-\frac{\sqrt{2}}{4}}=\\\\\frac{1}{\frac{\sqrt{6}-\sqrt{2}}{4}}=\\\\\boxed{\frac{4}{\sqrt{6}-\sqrt{2}}}$