Вычислите: (cos20+sin50-cos80)/корень(1+cos280)

Question

Вычислите: (cos20+sin50-cos80)/корень(1+cos280)

Answer 1

(cos20+sin50-cos80)/√(1+cos^2(80))=

=((cos20-cos80)+sin50)/√(1+cos^2(80))=

=(-2sin50*sin30)+sin50)/√(1+cos^2(80))=

=(-sin50+sin50)/√(1+cos^2(80))=0/√(1+cos^2(80))=0