Question 2
(a) Prove that $\sqrt2(\sin t+\cos t)\ge2\sqrt[4]{\sin2t}$ for every $0\le t\le\pi/2$.
(b) Find $y$ such that $1+\dfrac{2\cot2y}{\cot y}\ge\dfrac{\tan2y}{\tan y}$ “for every $y\in(0,\pi)$.”
(b) Find $y$ such that $1+\dfrac{2\cot2y}{\cot y}\ge\dfrac{\tan2y}{\tan y}$ “for every $y\in(0,\pi)$.”