Question

Упростите выражение: cos5a+cos6a+cos7a/sin5a+sin6a+sin7a

Answer 1

$frac{cos5a+cos6a+cos7a}{sin5a+sin6a+sin7a} = \ = frac{(cos5a+cos7a)+cos6a}{(sin5a+sin7a)+sin6a} = \ = frac{2cos frac{5a + 7a}{2}cos frac{5a - 7a}{2} + cos6a}{2sinfrac{5a + 7a}{2}cos frac{5a - 7a}{2} + sin6a} = \ = frac{2cos 6a times cos a + cos6a}{2sin6a times cos a+ sin6a} = \ = frac{cos 6a (2cos a + 1)}{sin6a( 2cos a+ 1)} = ctg6a$

Ответ: сtg 6a