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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