Question

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

[MNR 1976; Pb. CET 1996]

• A. 0
• B.
• C. 1/2
• D.

Answer 1

The correct option is B

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

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

$\Rightarrow$ $-\sqrt{2}\le cos(\theta -\frac{\pi }{4})\le \sqrt{2}$

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