solve the equation cos x + sin x \(\frac{1}{cos x - sinx}\) for values of such that 0 \(\leq\) x < 2\(\pi\)

A.

\(\frac{\pi}{2}\), \(\frac{3\pi}{2}\)

B.

\(\frac{\pi}{3}\), \(\frac{2\pi}{3}\)

C.

0, \(\frac{\pi}{3}\)

D.

0, \(\pi\)

Correct answer is D

cos x + sin x \(\frac{1}{cos x - sinx}\)

= (cosx + sinx)(cosx - sinx) = 1

= cos2x + sin2x = 1

cos2x - (1 - cos2x) = 1

= 2cos2x = 2

cos2x = 1

= cosx = \(\pm\)1 = x

= cos-1x (\(\pm\), 1)

= 0, \(\pi\) \(\frac{3}{2}\pi\), 2\(\pi\)

(possible solution)