The most general values of for which are given by

MATHEMATICS · Single correct · CBSE · Mathematics · Applications of Derivatives · Applications of Derivatives

Problem

The most general values of

x

for which

\sin x+\cos x=\min_{a\in\mathbb{R}}\left[1,a^2-4a+6\right]

are given by (1)

2n\pi

(2)

2n\pi+\frac{\pi}{2}

(3)

n\pi+(-1)^n\frac{\pi}{4}-\frac{\pi}{4}

(4) None of these