Question

Comprueben la siguiente identidad trigonométrica. (1−cos(A))(1+sec(A))cot(A)=sen(A)

Answer 1

Aplicando: sec (A) = 1 / cos (A)
cot (A) = cos (A) / sen (A)
(1-cos (A))*(1+1/cos (A))*(cos (A) /sen (A))
(1-cos (A))*((cos (A) + 1) / sen (A) )
(cos (A) - cos^2 (A) + 1 - cos (A) )/sen (A)
Simplificando Cos (A)
( -cos^2 (A) + 1) / sen (A)
Aplicando la identidad trigonométrica
(Cos^2 (A) = 1 - sen^2 (A)) y reemplazando
( -1 + sen^2 (A) +1)/sen (A)
(Sen^2 (A))/Sen (A)
= Sen (A)