Cos(-a)sina(1+ctg^2(-a))=ctga доказать тождество

Question

Cos(-a)sina(1+ctg^2(-a))=ctga доказать тождество

Answer 1

Cos(-a)sin(a)(1+ctg^2(-a))=cos(a)*sin(a)(1+ctg^2(-a))=cos(a)sin(a)(1+(cos^2(-a)/(sin^2(-a))))=cos(a)sin(a)(1+cos^2(a)/sin^2(a))=cos(a)sin(a)(sin^2(a)+cos^2(a))/sin^2(a)=cos(a)sin(a)/sin^2(a)=cos(a)/sin(a)=ctg(a)