Réponse :

Explications étape par étape :

cos(π/2 - α) = sin(α)

sin(5π/2 - α) = sin(2π + π/2 - α) = sin(π/2 - α) = cos(α)

tg(3π + α) = tg(2π + π + α) = tg(π + α) = sin(π+α)/cos(π+α)=tg(α)

sin(3π + α) = sin(2π + π + α) = sin(π + α) = -sin(α)

sin(3π/2 + α) =sin(2π - π/2 + α ) = sin(-(π/2-α))= -sin(π/2-α)=-cos(α)

cotg(π/2-α)=cos(π/2-α)/sin(π/2-α)=sin(α)/cos(α)=tg(α)

(sin(α) x cos(α) x tg(α))/(-sin(α) x (-cos(α)) x tg(α))

= 1