solve the equation cos x + sin x (frac{1}{cos x – sinx}) for values of such that 0 (leq) x

A.
(frac{pi}{2}), (frac{3pi}{2}) 
B.
(frac{pi}{3}), (frac{2pi}{3}) 
C.
0, (frac{pi}{3}) 
D.
0, (pi)
Correct Answer: Option D
Explanation
cos x + sin x (frac{1}{cos x – sinx})
= (cosx + sinx)(cosx – sinx) = 1
= cos^{2}x + sin^{2}x = 1
cos^{2}x – (1 – cos^{2}x) = 1
= 2cos^{2}x = 2
cos^{2}x = 1
= cosx = (pm)1 = x
= cos^{1}x ((pm), 1)
= 0, (pi) (frac{3}{2}pi), 2(pi)
(possible solution)