Question

сделайте алгебру быстрее

Answer 1

$cos^2alpha+mathrm{mathop{ctg}}^2alpha+sin^2alpha=1+mathrm{mathop{ctg}}^2alpha=1+dfrac{cos^2alpha}{sin^2alpha}=dfrac{sin^2alpha+cos^2alpha}{sin^2alpha}=\=dfrac1{sin^2alpha}\ alpha=dfrac{pi^{phantom{|}}}6:quaddfrac1{sin^2alpha}=dfrac1{(1/2)^2}=4$