Answer:
d. 60° , 120°
Step-by-step explanation:
[tex]cosx \: - \sqrt{1 - 3 {cos}^{2}x} =0[/tex]
[tex]cosx \: = \sqrt{1 - 3 {cos}^{2}x} [/tex]
Square both sides
[tex] {cos}^{2}x \: = 1 - 3 {cos}^{2}x [/tex]
Colliext like terms
[tex] {cos}^{2}x \: + 3 {cos}^{2}x = 1 [/tex]
[tex]4 {cos}^{2}x = 1[/tex]
Divide both sides by 4
[tex] {cos}^{2}x = \frac{1}{4} [/tex]
Take square roots of both sides
[tex]cos \: x = \sqrt{ \frac{1}{4} } = \frac{ + }{} \frac{1}{2} [/tex]
[tex]x = arc \: cos( \frac{1}{2}) = {60}^{o} [/tex]
[tex]or \: arc \: cos( - \frac{1}{2} ) = - {60}^{o} [/tex]
Cosine is negative in the second quadrant, therefore;
x = 180° - 60° = 120°
