The minimum value of + is - Vidyadip

MCQ

The minimum value of $\cos \theta + \sin \theta $ is

A
$0$
✓
$ - \sqrt 2 $
C
$1/2$
D
$\sqrt 2 $

✓

Answer

Correct option: B.

$ - \sqrt 2 $

b
(b) Let $f(x) = \cos \theta + \sin \theta = \sqrt 2 \cos \left( {\theta - \frac{\pi }{4}} \right)$

Since $ - 1 \le \cos \left( {\theta - \frac{\pi }{4}} \right) \le 1$

==> $ - \sqrt 2 \le \sqrt 2 \cos \left( {\theta - \frac{\pi }{4}} \right) \le \sqrt 2 $

Thus, the minimum value of $f(x)$ is $ - \sqrt 2 $.

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