Question

se secx=4, com 0 ≤ x < π/2, quanto vale tg2x?
por favor me ajudem

Answer 1

$cos(x)=\frac{1}{sec(x)}\\ \\ cos(x)=\frac{1}{4}\\ \\ sen(x)=\sqrt{1-cos^2(x)}\\ \\ sen(x)=\sqrt{1-(\frac{1}{4})^2}\\ \\ sen(x)=\sqrt{1-\frac{1}{16}}\\ \\ sen(x)=\sqrt{\frac{15}{16}}\\ \\ sen(x)=\frac{\sqrt{15}}{4}\\ \\ tg(x)=\frac{sen(x)}{cos(x)}=\frac{\frac{\sqrt{15}}{4}}{\frac{1}{4}}=\sqrt{15}$