Problem

Source: MDA TST 2016, 9

Tags: algebra



Let $\alpha \in \left( 0, \dfrac{\pi}{2}\right)$.Find the minimum value of the expression $$ P = (1+\cos\alpha)\left(1+\frac{1}{\sin \alpha} \right)+(1+\sin \alpha)\left(1+\frac{1}{\cos \alpha} \right) .$$