Question

calcule.........

sen^2x=1/2

Answer 1

$\mathrm{sen^{2}\,}x=\dfrac{1}{2}\\ \\ \\ \mathrm{sen\,}x=\pm \sqrt{\dfrac{1}{2}}\\ \\ \\ \mathrm{sen\,}x=\pm \dfrac{1}{\sqrt{2}}$


Multiplicando o numerador e o denominador por $\sqrt{2},$ temos

$\mathrm{sen\,}x=\pm \dfrac{\sqrt{2}}{\sqrt{2}\cdot \sqrt{2}}\\ \\ \\ \mathrm{sen\,}x=\pm \dfrac{\sqrt{2}}{2}\\ \\ \\ \begin{array}{rcl} \mathrm{sen\,}x=\dfrac{\sqrt{2}}{2}&\;\text{ ou }\;&\mathrm{sen\,}x=-\dfrac{\sqrt{2}}{2} \end{array}\\ \\ \\ \boxed{\begin{array}{crclc}\\ &x=\dfrac{\pi}{4}+\dfrac{k\pi}{2}&\\ \\ \end{array}}$

com $k$ inteiro.