Question

Срочно)!!!!
вычислить tg(0.5 arccos (-4/17))

Answer 1

$tg(frac{1}{2}arccos(-frac{4}{17}))=?\\tgfrac{ alpha }{2}= frac{sin alpha }{1+cos alpha } ; ; ,; ; alpha =arccos(-frac{4}{17})\\arccos(-frac{4}{17})=pi -arccosfrac{4}{17}; ; Rightarrow \\\sin(arccos(-frac{4}{17}))=sin(pi -arccosfrac{4}{17})=sin(arccosfrac{4}{17})=\\=sqrt{1-cos^2(arccosfrac{4}{17})}=sqrt{1-( frac{4}{17} )^2}=sqrt{1- frac{16}{289} }=frac{sqrt{273}}{17}\\\cos(arccos(-frac{4}{17}))=cos(pi -arccosfrac{4}{17})=-cos(arccosfrac{4}{17})=-frac{4}{17}$

$tg(frac{1}{2}arctg(-frac{4}{17}))=tg frac{ alpha }{2} = frac{frac{sqrt{273}}{17}}{1-frac{4}{17}} = frac{sqrt{273}cdot 17}{17cdot 13} = frac{sqrt{273}}{17}$