Question

Situación problemática 02:

Siendo tg(x +20°) = cotg(x - 10°). Hallar el valor de x.​

Answer 1

Respuesta:

x = -50º   ó   x=310º

Explicación paso a paso:

$\tan\left(x+20\right)&=\cot\left(x-10\right)\\\tan\left(x+20\right)&=\cfrac{1}{\tan\left(x-10\right)}\\\arctan\left[\tan\left(x+20\right)\right]&=\arctan\left[\cfrac{1}{\tan\left(x-10\right)}\right]\\x+20&=-\cfrac{\text{\ensuremath{\pi}}}{2}-\arctan\left(\tan\left(x-10\right)\right)\\x+20&=-90-\left(x-10\right)\\x+20&=-90-x+10\\x+x&=-90+10-20\\2x&=-100\\x&=-50\text{ \phantom{0} o \phantom{0}}x=360-50=310$