Question

The solution of the equation \(\sin x + \cos x = 0\) in \([0,2\pi]\) is:

• A. \(\pi/4,\,5\pi/4\)
• B. \(3\pi/4,\,7\pi/4\)
• C. \(\pi/2,\,3\pi/2\)
• D. \(\pi/4,\,7\pi/4\)

Hint:

Use \(\tan x = \frac{\sin x}{\cos x}\) to simplify.

Answer 1

The Correct Option is B

\[ \sin x = -\cos x \Rightarrow \tan x = -1 \] \[ x = \frac{3\pi}{4},\ \frac{7\pi}{4} \]