Find all solutions of the equation in the interval 0 2pi 2 c

Find all solutions of the equation in the interval [0, 2pi). (2 cos x - Squareroot 3) (2 sin x - Squareroot 2) = 0 Write your answer in radians in terms of pi. If there is more than one solution, separate them with commas.

Solution

By zero factor theorem, we have :

cosx = sqrt(3)/2
sin(x) = sqrt(2)/2

cosx = sqrt(3)/2 first :
We know x = pi/6
Also, cos is positive in quad 4
So, other value = 2pi - pi/6 or 11pi/6

sinx = sqrt2/2
We know x = pi/4
And sin is positive in quad 2
So, other value = pi - pi/4 = 3pi/4

So, answers are :
pi/6 , pi/4 , 3pi/4 , 11pi/6