Решебник по алгебре и начала математического анализа 11 класс Колягин Задание 109

\[1)\ y = 1 - 2\sin^{2}x\]

\[y = \cos{2x}\]

\[- 1 \leq \cos{2x} \leq 1;\]

\[E(y) = \lbrack - 1;\ 1\rbrack.\]

\[2)\ y = 2\cos^{2}x - 1\]

\[y = \cos{2x}\]

\[- 1 \leq \cos{2x} \leq 1;\]

\[E(y) = \lbrack - 1;\ 1\rbrack.\]

\[3)\ y = 3 - 2\sin^{2}x\]

\[y = 2 + \cos{2x}\]

\[- 1 \leq \cos{2x} \leq 1\]

\[1 \leq 2 + \cos{2x} \leq 3;\]

\[E(y) = \lbrack 1;\ 3\rbrack.\]

\[4)\ y = 2\cos^{2}x + 5\]

\[y = \cos{2x} + 6\]

\[- 1 \leq \cos{2x} \leq 1\]

\[5 \leq \cos{2x} + 6 \leq 7;\]

\[E(y) = \lbrack 5;\ 7\rbrack.\]

\[5)\ y = \cos{3x}\sin x - \sin{3x}\cos x + 4\]

\[y = \sin(x - 3x) + 4 = 4 - \sin{2x}\]

\[- 1 \leq - \sin{2x} \leq 1\]

\[3 \leq 4 - \sin{2x} \leq 5;\]

\[E(y) = \lbrack 3;\ 5\rbrack.\]

\[6)\ y = \cos{2x}\cos x + \sin{2x}\sin x - 3\]

\[y = \cos(2x - x) - 3 = \cos x - 3\]

\[- 1 \leq \cos x \leq 1\]

\[- 4 \leq \cos x - 3 \leq - 2;\]

\[E(y) = \lbrack - 4;\ - 2\rbrack.\]