Type an exact answerSolution16cos2x 12 cos2x 1216 cos2x 12

(Type an exact answer.)

16cos^2x = 12

cos^2x = 12/16

cos^2x -12/16

using formula : a^2 -b^2 = (a-b)(a+b)

(cosx -sqrt(3)/2 )(cosx +sqrt(3)/2 ) =0

cosx = sqrt3/2 ----> x= pi/6 , 2pi -pi/6 = pi/6 , 11pi/6 ( cosx is +ve in Ist and IInd quadrant)

cosx = -sqrt3/2 ----> x= pi -pi/6 , pi+pi/6 = 5pi/6 , 7pi/6 ( cosx is -ve in IInd and IIrd quadrant)

Solution : x= pi/6 , 5pi/6 , 7pi/6 , 11pi/6 for x belonging to interval [0, 2pi)