Question

упростите tg(pi/2-a)/cos(2pi-a)*sin(3pi/2+a)/(tg(3pi/2-a)

Answer 1

a)sin(3π/2+α)/(tg(3π/2-α)=-cosα/ctgα=-sinα

Answer 2

Ответ:

$\dfrac{tg(\frac{\pi}{2}-a)}{cos(2\pi -a)}\cdot \dfrac{sin(\frac{3\pi}{2}+a)}{tg(\frac{3\pi}{2}-a)}=\dfrac{tga}{cosa}\cdot \dfrac{-cosa}{ctga}=-\dfrac{tga}{ctga}=-\dfrac{sina\cdot sina}{cosa\cdot cosa}=\\\\\\=-\dfrac{sin^2a}{cos^2a}=-tg^2a$