Question

Сделайте алгебру быстрее

Answer 1

$\cos^2\alpha+\mathrm{\mathop{ctg}}^2\alpha+\sin^2\alpha=1+\mathrm{\mathop{ctg}}^2\alpha=1+\dfrac{\cos^2\alpha}{\sin^2\alpha}=\dfrac{\sin^2\alpha+\cos^2\alpha}{\sin^2\alpha}=\\=\dfrac1{\sin^2\alpha}\\ \alpha=\dfrac{\pi^{\phantom{|}}}6:\quad\dfrac1{\sin^2\alpha}=\dfrac1{(1/2)^2}=4$