Find all real numbers in the interval [0, 2 pi] that satisfy the equation. cos^2

Question

Find all real numbers in the interval [0, 2 pi] that satisfy the equation. cos^2 x + 2 cos (x) + 1 = 0 A) {pi/4, 7 pi/4} B) {pi} C) {2 pi} D) {pi/2, 3 pi/2} 2 sin(x) cos(x) + cos(x) = 0 A) {pi/2, 7 pi/6, 3 pi/2, 11 pi/6} B) {pi/2, 5 pi/6, 3 pi/2, 1} C) {pi/2, 5 pi/6, 3 pi/2, 11 pi/6} D) No solution Find the exact value by using a half-angle identity. Use the formula: cos A/2 = x Squareroot 1 + cos (A)/2 cos (22.5 degree) A) 1/2 Squareroot 2 - Squareroot 2 B) -1/2 Squareroot 2 - Squareroot 2 C) 1/2 Squareroot 2 + Squareroot 2 D) -1/2 Squareroot 2 + Squareroot 2

Explanation / Answer

22 . cos2x +2cos x+1=0

(cos x +1)^2=0

cos x=-1

x=cos-1(-1)

X=pi

option B is the correct answer.

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