SOLUTION: Could you please help solve the following problem, Solve the equation on the interval [0,2pi}, Write as a solution set and in radians 6(cos^2)x-3=0

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Question 1012337: Could you please help solve the following problem,
Solve the equation on the interval [0,2pi}, Write as a solution set and in radians
6(cos^2)x-3=0

Answer by ikleyn(52858) About Me  (Show Source):
You can put this solution on YOUR website!
. 
6cos%5E2%28x%29-3 = 0  -----> 

cos%5E2%28x%29 = 3%2F6 = 1%2F2  ----->

cos(x) = +/- sqrt%282%29%2F2.

Thus the original equation deployed in two equations:


1. cos(x) = sqrt%282%29%2F2  ----->  The solutions in the given interval are x = pi%2F4  and  x = 7pi%2F4.


2. cos(x) = -sqrt%282%29%2F2  -----> The solutions in the given interval are x = 3pi%2F4  and  x = 5pi%2F4.


Answer. x = pi%2F4, 3pi%2F4, 5pi%2F4 and 7pi%2F4.