How do I solve 4sin^2(x)-2=0

Question

How do I solve this I get stuck at sin^2(x)=1/2

Answer 1

You're nearly there! sin^2(x)=1/2 is right. Take square root of each side: sin(x)=1/sqrt(2) or sqrt(2)/2. The angle whose sine is 0.7071 is 45 degrees. Draw an isosceles right-angled triangle. You can see that if the shorter sides have length 1, then the hypotenuse has length sqrt(2) and the sine and cosine of either 45 degree angle is 1/sqrt(2) (usually written sqrt(2)/2=0.7071).