Question

Нужна помощь с задачей номер 45

Answer 1

$star ; ; alpha =arcsin frac{4}{5}quad Rightarrow quad sin alpha = frac{4}{5}; ; Rightarrow \\cos alpha =sqrt{1-sin^2 alpha }=sqrt{1-frac{16}{25}}= frac{3}{5}; ; Rightarrow ; ; alpha =arccosfrac{3}{5}; ; star \\star star ; ; arccosx+arccos y=arccos (xy-sqrt{1-x^2}cdot sqrt{1-y^2}); ,\\ esli; x+ygeq 0; ; ; star star \\\arcsin frac{4}{5} +arccosfrac{1}{sqrt{50}} =arccos frac{3}{5}+arccos frac{1}{5sqrt2} =\\=arccosBig (frac{3}{5}cdot frac{1}{5sqrt2}-sqrt{1-frac{9}{25}}cdot sqrt{1-frac{1}{50}}Big )=$

$=arccos Big ( frac{3sqrt2}{50}-sqrt{frac{16}{25}}cdot sqrt{frac{49}{50} }Big )=arccosBig ( frac{3sqrt2}{50}-frac{4}{5}cdot frac{7}{5sqrt2}Big )=\\=arccos Big ( frac{3sqrt2}{50}-frac{28sqrt2}{50}Big )=arccosBig (frac{-25sqrt2}{50}Big )=arccos (- frac{sqrt2}{2} )=\\=pi -arccosfrac{sqrt2}{2}=pi -frac{pi}{4}=frac{3pi }{4}$