Question

2sin^2 2x=2 In the domain [0,2pi) What can x equal ( in radians).

Answer 1

Bear in mind that, when it comes to trigonometric functions, the location of the exponent can be a bit misleading, however recall that sin²(θ) is really [ sin( θ )]²,


$\bf 2sin^2(2x)=2\implies sin^2(2x)=\cfrac{2}{2} \\\\\\ sin^2(2x)=1\implies [sin(2x)]^2=1\implies sin(2x)=\pm\sqrt{1} \\\\\\ sin(2x)=\pm 1\implies sin^{-1}[sin(2x)]=sin^{-1}(\pm 1)$

$\bf \measuredangle 2x=sin^{-1}(\pm 1)\implies \measuredangle 2x= \begin{cases} \frac{\pi }{2}\\\\ \frac{3\pi }{2} \end{cases}\\\\ -------------------------------\\\\ \measuredangle 2x=\cfrac{\pi }{2}\implies \measuredangle x=\cfrac{\pi }{4}\qquad \qquad \qquad \qquad \measuredangle 2x=\cfrac{3\pi }{2}\implies \measuredangle x=\cfrac{3\pi }{4}$