5cos2x+6sin^2x,если ctgx=1/3

Зная ctgx найдем синус [latex]1)1+ctg^{2} x= \frac{1}{sin^2x} \\ sin^2x= \frac{1}{1+ctg^2x} = \frac{1}{1+(1/3) ^{2} } = \frac{1}{1+1/9} = \frac{1}{10/9} = \frac{9}{10} =0.9[/latex] [latex]2) cos2x=1-2sin^2x[/latex] [latex]3)5cos2x+6sin^2x=5(1-2sin^2x)+6sin^2x=5-10sin^2x+6sin^2x= \\ 5-4sin^2x=5-4*0.9=5-3.6=1.4[/latex]