1) [latex]cos alpha = frac{8}{17} \ tg alpha =? \ \ sin^2 alpha +cos^2 alpha =1 \ sin^2 alpha =1-cos^2 alpha \ sin^2 alpha =1-( frac{8}{17})^2 \ sin^2 alpha =1- frac{64}{289} \ sin^2 alpha = frac{225}{289} \ sin alpha = sqrt{ frac{225}{289}} \ sin alpha = frac{15}{17} [/latex] [latex]tg alpha = frac{sin alpha }{cos alpha} \ tg alpha = frac{ frac{15}{17}}{ frac{8}{17}} \ tg alpha = frac{15}{17}* frac{17}{8} \ tg alpha = frac{15}{8} [/latex] [latex] sqrt{tg^2 alpha +1} = sqrt{( frac{15}{8})^2+1} = sqrt{ frac{225}{64}+1}= sqrt{ frac{289}{64}}= frac{17}{8} [/latex] 2) [latex]a-b=? \ a=sin alpha \ b=1-4sin^2 alpha cos^2 alpha \ alpha =60^0 \ \ a=sin60^0= frac{ sqrt{3}}{2} \ \ sin^2 alpha +cos^2 alpha =1 \ cos^2 alpha =1-sin^2 alpha \ cos^2 alpha =1-( frac{ sqrt{3}}{2})^2 \ cos^2 alpha =1- frac{3}{4} \ cos^2 alpha = frac{1}{4} \ cos alpha = sqrt{ frac{1}{4}} \ cos alpha = frac{1}{2} \ \ b=1-4sin^2 alpha cos^2 alpha =1-4*( frac{ sqrt{3}}{2})^2* frac{1}{4}=1-4* frac{3}{4}* frac{1}{4} =1- frac{3}{4}= frac{1}{4} [/latex] [latex]a-b= frac{ sqrt{3}}{2}- frac{1}{4} = frac{2 sqrt{3}}{4} - frac{1}{4} = frac{2 sqrt{3}-1}{4} [/latex] 3) [latex]sin alpha =2 \ cos^2 alpha -2=? \ \ sin^2 alpha +cos^2 alpha =1 \ cos^2 alpha =1-sin^2 alpha \ cos^2 alpha =1-2^2 \ cos^2 alpha =1-4 \ cos^2 alpha =-3 \ \ cos^2 alpha -2=-3-2=-5[/latex]
