Question

One of the possible values of A, for which cos 2A = cos A, is ______.

Options

• 0°

• 30°

• 45°

• 90°

Answer 1

One of the possible values of A, for which cos 2A = cos A, is 0°.

Explanation:

(A) A = 0°

cos(2 × 0°) = cos 0° = 1

cos(0°) = 1

Since 1 = 1, the equation holds true.

(B) A = 30°

cos(2 × 30°) = cos 60° = 0.5

`cos(30^circ) = sqrt(3)/2 ≈ 0.866`

0.5 ≠ 0.866

(C) A = 45°

cos(2 × 45°) = cos 90° = 0

`cos(45^circ) = 1/sqrt(2) ≈ 0.707`

0 ≠ 0.707

(D) A = 90°

cos(2 × 90°) = cos 180° = –1

cos(90°) = 0

–1 ≠ 0