Question

Se senx =1/4 , então cos2x + sen2x é igual a:

Answer 1

$\boxed{\begin{array}{l}\sf sen(x)=\dfrac{1}{4}\implies sen^2(x)=\dfrac{1}{16}\\\sf cos(2x)=1-2sen^2(x)\\\sf cos(2x)=\dfrac{16}{16}-2\cdot\dfrac{1}{16}=\dfrac{16-2}{16}=\dfrac{14\div2}{16\div2}\\\sf cos(2x)=\dfrac{7}{8}\\\sf cos^2(2x)=\dfrac{49}{64}\\\sf sen^2(2x)=\dfrac{64}{64}-\dfrac{49}{64}\\\\\sf sen^2(2x)=\dfrac{15}{64}\\\sf sen(2x)=\sqrt{\dfrac{15}{64}}\\\sf sen(2x)=\dfrac{\sqrt{15}}{8}\end{array}}$

$\boxed{\begin{array}{l}\sf cos(2x)+sen(2x)=\dfrac{7}{8}+\dfrac{\sqrt{15}}{8}=\dfrac{7+\sqrt{15}}{8}\end{array}}$