Question

If \((\alpha,\beta)\subseteq\left(0,\dfrac{\pi}{2}\right)\) is the smallest set containing all the possible solutions of the inequality \[ \sin x+\cos2x>1, \] then \(\alpha+\beta=\)

• A. \(\dfrac{\pi}{2}\)
• B. \(\dfrac{\pi}{3}\)
• C. \(\dfrac{\pi}{6}\)
• D. \(\dfrac{\pi}{4}\)

Hint:

Whenever an inequality involves both \(\sin x\) and \(\cos2x\), first convert \[ \boxed{\cos2x=1-2\sin^2x} \] so that the inequality becomes a quadratic in \(\sin x\).

Answer 1

The Correct Option is C