Find the solutions of the equation 2 cos x 1 0 x 4 pi3 n

Find the solutions of the equation. 2 cos x - 1= 0 x = 4 pi/3 + n pi or x = 5 pi/6 n pi x = pi/3 + n pi or x = 5 pi/3 n pi x = 4 pi/3 + 2n pi or x = 5 pi/6 2n pi x = pi/3 + 2n pi or x = 5 pi/3 2n pi Find the exact value by using a difference identity. tan 285 degree -2 - squareroot 3 2 - squareroot 3/4 2 + squareroot 3 2 + squareroot 3/4

Solution

1) 2cosx -1 =0
cosx = 1/2

x= pi/3 , 2pi -pi/3 = pi/3 , 5pi/3

General solution x = pi/3 +2pi*k ; x = 5pi/3 +2pi*k

Option D

2)