Question

4 sen x = 12 sen^2 x -1​

Answer 1

Respuesta:

Explicación paso a paso:

$\textbf{La expresi\'on es:}\\\\4\sin(x)=12\sin^{2}(x)-1\\\textbf{Transponiendo:} \\\\-12\sin^{2}(x)+4\sin(x)+1=0\\\textbf{Usando la f\'ormula general con a=-12,b=4,c=1}\\\\\sin(x)=\frac{-4\pm\sqrt{(4)^{2}-4(-12)(1)}}{2(-12)}\\\sin(x)=\frac{-4\pm\sqrt{16+48}}{-24}\\\sin(x)=\frac{-4\pm\sqrt{64}}{-24}\\\sin(x)=\frac{-4\pm 8}{-24}\\\sin(x)=\frac{-4+8}{-24}=\frac{4}{-24}=\frac{1}{-6}\\x=\sin^{-1}(\frac{1}{-6})=-9^{\circ}35'38" \\\\\sin(x)=\frac{-4-8}{-24}=\frac{-12}{-24}=\\=\frac{1}{2}\\\\x=\sin^{-1}(\frac{1}{2})=30^{\circ}$