Question

Dado que sen x + cos x = 2/5, o valor de sen(2x) é:

Answer 1

$\displaystyle \sf sen\ x + cos\ x = \frac{2}{5} \\\\\ sen(2x) = ? \\\\ \underline{\text{Elevando a express{\~a}o ao quadrado, temos}}: \\\\ (sen\ x+cos\ x) ^2=\left(\frac{2}{5}\right)^2 \\\\\\ sen^2x+cos^2x+2\cdot sen\ x\cdot cos\ x=\frac{4}{25} \\\\\\ 1+sen(2x) = \frac{4}{25} \\\\\\ sen(2x)=\frac{4}{25}-1 \\\\\\ sen(2x)=\frac{4-25}{25} \\\\\\ \boxed{\sf sen(2x)=\frac{-21}{25}}\checkmark$