The solution set for the equation cos x squareroot 32 is pi

The solution set for the equation cos x = squareroot 3/2 is {pi/6, 11x/6}. Use this information to solve the following equation over the interval [0, 2x). cos 2x = squareroot 3/2 Select the correct choice below and, if necessary. fill in the answer box to complete your choice.

Solution

cos2x = sqrt3/2

2x = 2k*pi +pi/6

x= k*pi +pi/12

= ( 12k*pi + pi)/12

2x = 2k*pi + 2pi - pi/6 = 2k*pi +11pi/6

2x = 2k*pi +11pi/6

x = k*pi +11pi/12

x = (12k*pi +11pi)/12

plug k = 0 ; x = pi/12 , 11pi/12, 13pi/12