SMO 2011 Senior Round 1 Question 2
SMO · SMO 2011 Senior Round 1
Suppose $\theta$ is an angle between $0$ and $\pi/2$, and $\sin2\theta=a$. Which expression equals $\sin\theta+\cos\theta$?
$\sqrt{a+1}$
$(\sqrt2-1)a+1$
$\sqrt{a+1}-\sqrt{a^2-a}$
$\sqrt{a+1}+\sqrt{a^2-a}$
None of the above.