The greatest value of sin x + cos x is:

Correct option is C

Given:

Expression to maximize: sin x + cos x

Formula Used:

​$$\sin^2 x + \cos^2 x = 1$$​

Solution:

​$$(\sin x + \cos x)^2 = 1 + 1 = 2$$​

​$$\sin x + \cos x = \sqrt{2}$$​

The greatest value of sin x + cos x is $$\sqrt{2}$$​​