Найдите Tg (а + П/4) , если cos2a=1/3 ; a э (0; П/2)

cos 2a = 1/32cos²a - 1 =1/32cos²a = 4/3cos²a = 2/3tg²a + 1 = [latex] frac{1}{cosвa} [/latex]tg²a = [latex] frac{1-cosвa}{cosвa} [/latex]tga = [latex] sqrt{ frac{1-cosвa}{cosвa}}= sqrt{ frac{ frac{1}{3} }{ frac{2}{3}} } = sqrt{ frac{1}{2} } = frac{1}{ sqrt{2} } [/latex]tg(a + π/4) = [latex] frac{tga+tg frac{pi}{4} }{1-tga*tg frac{pi}{4}} = frac{ frac{1}{ sqrt{2} } +1}{1- frac{1}{ sqrt{2}}} = frac{ frac{ sqrt{2}+1}{sqrt{2}} }{ frac{ sqrt{2}-1}{sqrt{2}} } = frac{ sqrt{2}+1}{ sqrt{2}-1} = [/latex][latex] frac{2+2 sqrt{2} +1}{ 2 -1в} =3+2 sqrt{2} [/latex]