Cos11a+3cos9a+3cos7a+cos5a/cos8a если cosa=1/3

Ответ:

8/27

Объяснение:

$\frac{cos11a+3cos9a+3cos7a+cos5a}{cos8a}= \frac{(cos11a+cos5a)+3(cos9a+cos7a)}{cos8a}=\\ \\ \\ \frac{2cos\frac{11a+5a}{2}*cos\frac{11a-5a}{2} +3*2cos\frac{9a+7a}{2}*cos\frac{9a-7a}{2}}{cos8a}=\\ \\ \\ \frac{2cos8acos3a+6cos8acosa}{cos8a}=2cos3a+6cosa=2*(4cos^3a-3cosa)+6cosa=\\ \\ \\ 8cos^3a=8*(\frac{1}{3})^3=\frac{8}{27}$