Question

Вычислите 4√5 tg(arccos2/3)

Answer 1

$4sqrt5, tg(arccos frac{2}{3} )=?\\ alpha =arccos frac{2}{3}; ; ; Rightarrow ; ; ; cos alpha =frac{2}{3}\\1+tg^2 alpha =frac{1}{cos^2alpha }quad Rightarrow quad tg^2 alpha = frac{1}{cos^2 alpha } -1\\tg^2 alpha = frac{1}{(frac{2}{3})^2} -1= frac{9}{4} -1= frac{5}{4} \\tg alpha =pm sqrt{ frac{5}{4} }=pm frac{sqrt5}{2} \\tg(arccos frac{2}{3} )=pm frac{sqrt5}{2}$

$4sqrt5, tg(arccos frac{2}{3})=pm , 4sqrt5cdot frac{sqrt5}{2} =pm frac{4cdot 5}{2} =pm 10$