Упростите выражение:(1-〖cos〗^2 α)/(〖sin〗^2 α)+1/(〖sin〗^2 α*(1+〖tg〗^2 α))

Question

Упростите выражение:(1-〖cos〗^2 α)/(〖sin〗^2 α)+1/(〖sin〗^2 α*(1+〖tg〗^2 α))

Answer 1

(1-cos^2 α)/(sin^2 α)+1/(sin^2 α*(1+tg^2 α))

1-cos^2 α=sin^2α

1+tg^2 α=1/(cos^2a)

(1-cos^2 α)/(sin^2 α)+1/(sin^2 α*(1+tg^2 α))=sin^2α/(sin^2 α)+

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