Question

Упростите выражения:

а) tg (180градусов-α) / ctg(90 градусов-α)

б) сos²(90градусов-α)-1 / cos (180градусов -α)

в) sin (π-α) / tg (π+α)

г) tg (π-α)/ ctg (π/2 - α)

д) sin² (180 градусов-α)-1 / cos(360градусов-α)

е) ctg (π+α)-cos(90градусов+α) / tg ( 3π/2-α).

Спасибо.

Answer 1

а) $frac{tg(180- alpha )}{ctg(90- alpha )}= frac{-tg alpha }{tgalpha}=-1$

б) $frac{cos^2(90- alpha )-1}{cos (180- alpha )} = frac{sin^2 alpha -1}{cos (180- alpha )} = frac{sin^2alpha -cos^2 alpha -sin^ alpha }{-cos alpha}= frac{ -cos^2 alpha }{-cos alpha}=cos alpha$

в)$frac{sin ( pi - alpha )}{ tg ( pi + alpha )} = frac{sin alpha }{tg alpha } =sin alpha * frac{cos alpha }{sin alpha } =cos alpha$

г)$frac{tg( pi - alpha )}{ctg( pi /2- alpha) } = frac{-tg alpha }{tg alpha } =-1$

д)$frac{sin^2 ( pi - alpha )-1}{cos(360- alpha )} = frac{sin^2 alpha -sin^2 alpha -cos^2 alpha }{cos alpha } = frac{-cos^2 alpha }{cos alpha } =-cos alpha$

е) $frac{ctg( pi + alpha )- cos( pi /2+ alpha) }{tg (3 pi /2- alpha )} = frac{ctg alpha -sin alpha }{ctg alpha } =1- frac{sin^2 alpha }{cos alpha }$