Question

Se sen(×)=4/5 e 0 <×<π/2, o valor da tg(2×) é:

Answer 1

Resposta:

$tg2x=-\frac{24}{7}$

Explicação passo a passo:

$0<x<\frac{\pi }{2} \\\\0<2x<\pi \implies cos2x<0,sec2x<0~e~tg2x<0\\\\cos2x=1-2sen^2x\\\\cos2x=1-2(\frac{4}{5})^2 \\\\cos2x=1-2.\frac{16}{25}\\\\cos2x=\frac{25-32}{25}\\\\cos2x=\frac{-7}{25}\implies sec2x=-\frac{25}{7} \implies sec^22x=\frac{625}{49} \\\\tg^22x=sec^22x-1\\\\tg^22x=\frac{625}{49}-1\\\\tg^22x=\frac{625-49}{49}\\\\tg^22x=\frac{576}{49}\\\\tg2x=-\frac{24}{7}$