Решебник по алгебре и начала математического анализа 11 класс Колягин Задание 123

\[1)\ y = \cos^{4}x - \sin^{4}x\]

\[y = \left( \cos^{2}x - \sin^{2}x \right)\left( \cos^{2}x + \sin^{2}x \right)\]

\[y = \cos{2x} \cdot 1 = \cos{2x}.\]

\[Ответ:\ - 1;\ 1.\]

\[2)\ y = \sin\left( x + \frac{\pi}{4} \right)\sin\left( x - \frac{\pi}{4} \right)\]

\[y = \frac{1}{2}\left( \cos\frac{\pi}{2} - \cos{2x} \right) = - \frac{1}{2}\cos{2x}.\]

\[Ответ:\ - \frac{1}{2};\ \frac{1}{2}.\]

\[3)\ y = 1 - 2\left| \sin{3x} \right|\]

\[0 \leq \left| \sin{3x} \right| \leq 1\]

\[- 2 \leq - 2\left| \sin{3x} \right| \leq 0\]

\[- 1 \leq 1 - 2\left| \sin{3x} \right| \leq 1.\]

\[Ответ:\ - 1;\ 1.\]

\[4)\ y = \sin^{2}x - 2\cos^{2}x\]

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

\[y = 1 - 3\cos^{2}x\]

\[0 \leq \cos^{2}x \leq 1\]

\[- 3 \leq - 3\cos^{2}x \leq 0\]

\[- 2 \leq 1 - 3\cos^{2}x \leq 1.\]

\[Ответ:\ - 2;\ 1.\]