Question

Solve the equation for all real values of x.

a.pi/6
b.pi k,pi/6
c. pik
d.pi/6+pik

Answer 1

C

Explanation:

1 / (cos x - sin x) = cos x + sin x

Multiply:

1 = (cos x + sin x) (cos x - sin x)

Distribute:

1 = cos² x - sin² x

Use trig identity:

sin² x + cos² x = cos² x - sin² x

2 sin² x = 0

sin x = 0

x = πk

Answer C.