Question

Срочно 30 штук, алгебра

Answer 1

Ответ:

Объяснение:

$frac{sin(5alpha )-sin(alpha) }{sin(5alpha)*cos(3alpha )-cos5(alpha )*sin(3alpha) }$

Упростим числитель:

$sin(5alpha )-sin(alpha )=2*sinfrac{5alpha -alpha }{2} *cosfrac{5alpha +alpha }{2} =2*sin(2alpha )*cos(3alpha ).$

Упростим знаменатель:

$sin(5alpha )*cos(3alpha )-sin(3alpha )*cos(5alpha )=\=frac{1}{2}*(sin(5alpha -3alpha )+sin(5alpha +3alpha ))-frac{1}{2} *(sin(3alpha -5alpha )+sin(3alpha +5alpha ))=\=frac{1}{2} *(sin(2alpha )+sin(8alpha ))-frac{1}{2} *(sin(-2alpha )+sin(8alpha ))=\=frac{1}{2} *(sin(2alpha )+sin(8alpha ))-frac{1}{2} *(-sin(2alpha )+sin(8alpha ))=\=frac{1}{2}*(sin(2alpha )+sin(8a)+sin(2alpha )-sin(8alpha ))=frac{1}{2} *2*sin(2alpha )=sin(2alpha ).$

Следовательно:

$frac{2*sin(2alpha)*cos(3alpha ) }{sin(2alpha )} =2*cos(3alpha ).$