Вычислите значение функции y: [latex]y=sin^{4} x + cos^{4}x [/latex] , если tg x = 2

[latex]tg^2x + 1 = \frac{sin^2x}{cos^2x} + 1 = \frac{sin^2x + cos^2x}{cos^2x} = \frac{1}{cos^2x} =\ \textgreater \ cos^2x = \frac{1}{1+tg^2x} cos^2x = 1 -sin^2x [/latex] [latex]1 - sin^2x = \frac{1}{1+tg^2x} =\ \textgreater \ [/latex] [latex]1 - \frac{1}{1+tg^2x} = \frac{1+tg^2x - 1}{1 + tg^2x} = \frac{tg^2x}{1+ tg^2x} = sin^2x y = sin^4x + cos^4x = (\frac{tg^2x}{1+ tg^2x})^2 + (\frac{1}{1+tg^2x})^2 = (\frac{4}{5})^2 + ( \frac{1}{5})^2 = \frac{17}{25} [/latex]