Question

Halla "x" que cumple:
sec²x + csc²x-2= 2ctg²x​

Answer 1

Respuesta:

$S=\{x=\frac{\pi }{4}+2k\pi ,k\n\in~Z\}$

Explicación paso a paso:

sec²x + csc²x - 2 = 2ctg²x​

sec²x + csc²x - 2 = 2(csc²x - 1)

sec²x + csc²x - 2 = 2csc²x - 2

sec²x = 2csc²x - csc²x

sec²x = csc²x

$\frac{1}{cos\?\²x}=\frac{1}{sen^2x}\\\\ cos^2x = sen^2x \\\\cosx=\pm senx\\\\cosx=senx\implies x=\frac{\pi }{4} +2k\pi,~ ~k~\in Z\\\\ou~~cosx = -senx\\\\cosx=sen(-x)\\\\sen(\frac{\pi }{2}-x) =sen(-x)\\\\\frac{\pi }{2}-x=-x+2k\pi\\\\\frac{\pi }{2} =2k\pi ,n\tilde ao~ h\'a~ x$