\frac { \sin 4 A + \sin 5 A + \sin 6 A } { \cos 4 A + \cos 5 A + \cos

1.	\frac { \sin 4 A + \sin 5 A + \sin 6 A } { \cos 4 A + \cos 5 A + \cos 6 A } = \tan 5 A
Answer» (sin4a + sin5a + sin6a) / (cos4a + cos5a + cos6a) = = (2sin ((4a + 6a) / 2) * cos ((6a-4a) / 2) + sin5a) / (2cos ((4a + 6a) / 2) * cos ((6a-4a) / 2) + cos5a) = = (2sin5a * cosa + sin5a) / (2cos5a * cosa + cos5a) = = (sin5a (2cosa + 1)) / (cos5a (2cosa + 1)) = sin5a / cos5a = tan5a

\frac { \sin 4 A + \sin 5 A + \sin 6 A } { \cos 4 A + \cos 5 A + \cos 6 A } = \tan 5 A

Answer»

(sin4a + sin5a + sin6a) / (cos4a + cos5a + cos6a) =

= (2sin ((4a + 6a) / 2) * cos ((6a-4a) / 2) + sin5a) / (2cos ((4a + 6a) / 2) * cos ((6a-4a) / 2) + cos5a) =

= (2sin5a * cosa + sin5a) / (2cos5a * cosa + cos5a) =

= (sin5a (2cosa + 1)) / (cos5a (2cosa + 1)) = sin5a / cos5a = tan5a