\[1)\ 0{^\circ} < a < 90{^\circ}\ \ \]
\[\cos a > 0.\]
\[90{^\circ} < b < 180{^\circ}\ \ \ \]
\[\cos b < 0.\]
\[Ответ:\ \ да.\]
\[2)\ \sin{45{^\circ}} = \sin(90{^\circ} - 45{^\circ}) =\]
\[= \cos{45{^\circ}}.\]
\[Ответ:\ \ да.\]
\[3)\ \sin^{2}a + \cos^{2}a = 1\ \ \ \]
\[\sin a = 0:\]
\[\cos a = 1 - 0^{2} = 1.\]
\[Ответ:\ \ нет.\]
\[4)\ 90{^\circ} < a < 180{^\circ}\ \ \ \]
\[\cos a < 0.\]
\[Ответ:\ \ да.\]
\[5)\ 0{^\circ} < a < 180{^\circ}\ \ \]
\[\sin a > 0.\]
\[Ответ:\ \ нет.\]
\[6)\ \cos a = 0:\ \ \ \]
\[a = 90{^\circ}.\]
\[Ответ:\ \ да.\]
\[7)\ \sin a = 0:\ \ \ \]
\[a_{1} = 0{^\circ};\ \ \ \]
\[a_{2} = 180{^\circ}.\]
\[Ответ:\ \ нет.\]
\[8)\ \cos a = - 1:\ \ \ \]
\[a = 180{^\circ}.\]
\[Ответ:\ \ нет.\]
\[9)\ \sin a = 1:\ \ \ \]
\[a = 90{^\circ}.\]
\[Ответ:\ \ да.\]
\[10)\ \sin{90{^\circ}} = 1:\ \ \ \]
\[0{^\circ} \leq a < 90{^\circ}\ \ \ \]
\[90{^\circ} < a \leq 180{^\circ}\ \ \]
\[\sin a < 1.\]
\[Ответ:\ \ да.\]
\[11)\ \cos{180{^\circ}} = - 1:\ \ \ \]
\[0{^\circ} \leq a < 180{^\circ}\ \ \ \]
\[\cos a > - 1.\ \]
\[Ответ:\ \ да.\]
\[12)\ \sin(180{^\circ} - a) = \sin a.\]
\[Ответ:\ \ да.\]
\[13)\ \cos(180{^\circ} - a) = - \cos a.\]
\[Ответ:\ \ да.\]
\[14)\ \cos{45{^\circ}} = \cos(360{^\circ} - 45{^\circ}) =\]
\[= \cos{315{^\circ}}.\]
\[Ответ:\ \ нет.\]
\[15)\ \sin{45{^\circ}} = \sin(180{^\circ} - 45{^\circ}) =\]
\[= \sin{135{^\circ}}.\]
\[Ответ:\ \ нет.\]
\[16)\ 0{^\circ} < a < 90{^\circ}:\ \ \ \]
\[tg\ a > 0.\ \ \ \]
\[90{^\circ} < b < 180{^\circ}:\ \ \]
\[tg\ b < 0.\]
\[Ответ:\ \ да.\]
\[17)\ 0{^\circ} < a < 90{^\circ}:\ \ \ \]
\[tg\ a > 0.\ \ \ \]
\[90{^\circ} < b < 180{^\circ}:\ \ \ \]
\[ctg\ b < 0.\]
\[Ответ:\ \ да.\]