Question

Which of the following is a solution to 2cos^2x– 2 = 0 ?

A.0°
B.30°
C.180°
D.330°​

Answer 1

2 possible results

0° and 180°

Explanation:

2cos² x– 2 = 0 (add 2 to both sides)

2cos² x = 2 (divide both sides by 2)

cos² x = 2/2

cos² x = 1

cos x = ±√1

cos x = ±1

because the range of x is not stated, there are 2 possible results for x that will cause cos x to be either 1 or -1

0° and 180°

Answer 2

A and C

Explanation:

Given

2cos²x - 2 = 0 ( add 2 to both sides )

2cos²x = 2 ( divide both sides by 2 )

cos²x = 1 ( take the square root of both sides )

cos x = ±
`√(1)` = ± 1

cos x = 1 ⇒ x =
`cos^(-1)`(1) = 0°

cos x = - 1 ⇒ x =
`cos^(-1)`(- 1) = 180°