Answer:
see explanation
Step-by-step explanation:
note that (sinx)² = sin²x
4sin²x - 2 = 0 ( add 2 to both sides )
4sin²x = 2 ( divide both sides by 4 )
sin²x = [tex]\frac{2}{4}[/tex] = [tex]\frac{1}{2}[/tex] ( take square root of both sides )
sinx = ± [tex]\sqrt{\frac{1}{2} }[/tex] = ± [tex]\frac{1}{\sqrt{2} }[/tex]
sinx = [tex]\frac{1}{\sqrt{2} }[/tex] ( sinx > 0 , then x is in 1st/2nd quadrants )
x = [tex]\frac{\pi }{4}[/tex] , π - [tex]\frac{\pi }{4}[/tex] = [tex]\frac{3\pi }{4}[/tex]
sinx = - [tex]\frac{1}{\sqrt{2} }[/tex] ( sinx < 0 , then x is in 3rd/4th quadrants )
x = π + [tex]\frac{\pi }{4}[/tex] = [tex]\frac{5\pi }{4}[/tex] , 2π - [tex]\frac{\pi }{4}[/tex] = [tex]\frac{7\pi }{4}[/tex]
solutions are
[tex]\frac{\pi }{4}[/tex] , [tex]\frac{3\pi }{4}[/tex] , [tex]\frac{5\pi }{4}[/tex] , [tex]\frac{7\pi }{4}[/tex] in the interval [ 0, 2π )
