Question

Interval is 0, 2pi) 4 sin^2x-4 sin x + 1 = 0

Answer 1

`\large\boxed{x=(\pi)/(6)\ \vee\ x=(5\pi)/(6)}`

Explanation:

`4\sin^2x-4\sin x+1=0\\\\2^2\sin^2x-2(2\sin x)(1)+1^2=0\\\\(2\sin x)^2-2(2\sin x)(1)+1^2=0\qquad\text{use}\ (a-b)^2=a^2-2ab+b^2\\\\(2\sin x-1)^2=0\iff2\ain x-1=0\qquad\text{add 1 to both sides}\\\\2\sin x=1\qquad\text{divide both sides by 2}\\\\\sin x=(1)/(2)\to x=(\pi)/(6)\ \vee\ x=(5\pi)/(6)`