Question

Calcule cotg[arccotg(2) + 5π/2]. Muito obrigada a quem ajudar.

Answer 1

cotg(arccotg(2) + 5π/2) 
Seja arctg(2) = y => cotgy = 2 => tgy = 1/2$\frac{cos(y+ \frac{5 \pi }{2}) }{sen(y+ \frac{5 \pi }{2} )} = \frac{cosycos \frac{5 \pi }{2}-senysen \frac{5 \pi }{2} }{senycos \frac{5 \pi }{2} +sen \frac{5 \pi }{2} cosy} = \frac{cosy .0-seny.(-1)}{seny.0+(-1).cosy}= \\ \frac{seny}{-cosy} = -tgy = -1/2$