Solving trig identities

Question

Restriction from [0, 2pi).

 

4cos²x+2sin²x=3

Answer 1

4*cos^2(x) + 2*sin^2(x) = 3
2*cos^2(x) + 2*cos^2(x) + 2*sin^2(x) = 3

2*cos^2(x) + 2*(cos^2(x) + sin^2(x)) = 3

2*cos^2(x) + 2*1 = 3

2*cos^2(x) = 1

cos^2(x) = 1/2

cos(x) = +- sqrt(2)/2

 

Solutions with the + sign:

pi/4, 7pi/4

 

Solutions with the - sign:

3pi/4, 5pi/4

 

Final answer: {pi/4, 3pi/4, 5pi/4, 7pi/4}