Question

tg ( π/2 - x ) = cotg x

Answer 1

tg (π - x) = cotg x⇒
    2

tg (π  - x) = 1  ⇒
   2             tg x

tg (π - x) = tg x⇒
    2

tg² x = 1⇒

tg x = √1⇒

tg x = + 1 ou tg x = -1⇒

x ={ π + 2π}
      2
Bons Estudos
kélémen

Answer 2

Resposta:

Correto

Explicação passo-a-passo:

$tg(\dfrac{\pi}{2}-x)=\dfrac{sen(\dfrac{\pi}{2}-x)}{cos(\dfrac{\pi}{2}-x)}\\\\\\tg(\dfrac{\pi}{2}-x)=\dfrac{sen(\dfrac{\pi}{2}).cos(x)-sen(x).cos(\dfrac{\pi}{2}) }{cos(\dfrac{\pi}{2}).cos(x)+sen(\dfrac{\pi}{2}).sen(x)}\\\\\\tg(\dfrac{\pi}{2}-x)=\dfrac{1.cos(x)-sen(x).0}{0.cos(x)+1.sen(x)}\\\\\\tg(\dfrac{\pi}{2}-x)=\dfrac{cos(x)}{sen(x)}\\\\\\tg(\dfrac{\pi}{2}-x)=cotg(x)$