6.84 [latex]sin^2 alpha +cos^2 alpha =1quad implies quad sin^2 alpha =1-cos^2 alpha \ \ cos alpha = frac{3}{6}= frac{1}{2};qquad tg eta = frac{3}{4} \ \ \ frac{sin^2 alpha-4tg eta }{ sqrt{1-cos^2 alpha } } =frac{1-cos^2 alpha-4tg eta }{ sqrt{1-cos^2 alpha } } = frac{1-ig{( frac{1}{2}}ig )^2- 4 cdot ig{ frac{3}{4}}}{ sqrt{1-ig{( frac{1}{2}}ig )^2} } =frac{1-ig{ frac{1}{4}}- 3}{ sqrt{1-ig{ frac{1}{4}}} } =[/latex] [latex]=frac{1-ig{ frac{1}{4}}- 3}{ sqrt{1-ig{ frac{1}{4}}} } =frac{-ig{ 2frac{1}{4}} }{ sqrt{ig{ frac{3}{4}}} } =-2frac{1}{4} cdot sqrt{ frac{4}{3}} =- frac{9}{4} cdot frac{2}{sqrt{3}} =- frac{9 sqrt{3} }{6} =- frac{3 sqrt{3} }{2} [/latex] 6.85 [latex]sin^2 alpha +cos^2 alpha =1 quad implies quad sin^2 alpha =1-cos^2 alpha implies \ \ implies sin alpha = sqrt{1-cos^2 alpha} \ \ tg alpha = frac{ig {sin alpha }}{ig{cos alpha }} = frac{ig {sqrt{1-cos^2 alpha} }}{ig{cos alpha }} \ \ tg^2 alpha = frac{ig {1-cos^2 alpha }}{ig{cos^2 alpha }} \ \ frac{ig {1-cos^2 alpha }}{ig{cos^2 alpha }} = ig( -frac{5}{12}ig)^2 [/latex] [latex]\ \ frac{ig {1-cos^2 alpha }}{ig{cos^2 alpha }} = frac{25}{144} \ \ 144-144cdot cos^2 alpha =25cdot cos^2 alpha \ \ -169cdot cos^2 alpha =-144 /:(-169) \ \ cos^2 alpha = frac{144}{169}\ \ cos alpha = frac{12}{13} vee cos alpha = -frac{12}{13} [/latex]
