Sin (4a) +sin(5a)+sin(6a)/cos(4a)+cos(5a)+cos(6a) спростить

Question

Sin (4a) +sin(5a)+sin(6a)/cos(4a)+cos(5a)+cos(6a) спростить

Answer 1

sin4a + sin5a + sin6a = sin4a + sin6a + sin5a, 2sin (5a) * cosa + sin5a = sin5a (2cosa+1)

cos4a + cos5a + cos6a = cos4a + cos6a + cos5a, 2cos5a*cosa + cos5a = cos5a (2cosa+1)

sin5a (2cosa+1) / cos5a (2cosa+1) = sin5a/cos5a = tg5a