How do you find solutions of 4cos^2x=1?

Question

Zero is less than or equal to x and x is less than 360

 

I tried using different double angle identities but I can't figure out which to use and how to use it. 

Answer 1

In this case you only have Cos² X as a variable. So solve for COsX first and then X.

 No need for Simplification.

Answer 2

4cos²(x) = 1

 

This is a perfect square.  You don't need double angle identities.  Just take the square root of both sides.

 

√(4cos²(x)) = √1

2 cos(x) = 1

cos(x) = 1/2

 

For 0 < x < 360^o, there are two solutions:

 

x = (pi)/3 and 5(pi)/3 = 60^o and 300^o