Решебник по алгебре и начала математического анализа 10 класс Колягин Задание 1017

\[\boxed{\mathbf{1017.}}\]

\[1)\ tg( - a) \bullet \cos a + \sin a =\]

\[= - tg\ a \bullet \cos a + \sin a =\]

\[= - \frac{\sin a}{\cos a} \bullet \cos a + \sin a =\]

\[= - \sin a + \sin a = 0\]

\[2)\cos a - ctg\ a \bullet \left( - \sin a \right) =\]

\[= \cos a + ctg\ a \bullet \sin a =\]

\[= \cos a + \frac{\cos a}{\sin a} \bullet \sin a =\]

\[= \cos a + \cos a = 2\cos a\]

\[3)\ \frac{\cos( - a) + \sin( - a)}{\cos^{2}a - \sin^{2}a} =\]

\[= \frac{\cos a - \sin a}{\left( \cos a - \sin a \right)\left( \cos a + \sin a \right)} =\]

\[= \frac{1}{\cos a + \sin a}\]

\[4)\ tg( - a) \bullet ctg( - a) +\]

\[+ \cos^{2}( - a) + \sin^{2}a =\]

\[= tg( - a) \bullet \frac{1}{\text{tg}( - a)} + \cos^{2}a +\]

\[+ \sin^{2}a = 1 + 1 = 2\]