Question

Cos 11 a + cos 9 a+ 3 cos 7 a+ 3 cos 5 a/ cos 8 a

Answer 1

Ответ 8/17 Обьяснение не знаю

папа сказал

Answer 2

To simplify the given expression, we can use the trigonometric identity:

cos(A + B) = cos(A)cos(B) - sin(A)sin(B)

Using this identity, let's simplify the numerator first:

cos(11a) + cos(9a) + 3cos(7a) + 3cos(5a)

= [cos(8a + 3a) + cos(8a - a)] + [cos(8a + a) + cos(8a - 3a)] + 3cos(7a) + 3cos(5a)

= [cos(8a)cos(3a) - sin(8a)sin(3a)] + [cos(8a)cos(a) - sin(8a)sin(a)] + 3cos(7a) + 3cos(5a)

Now, let's simplify the denominator:

cos(8a)

Now, we can rewrite the expression as:

[(cos(8a)cos(3a) - sin(8a)sin(3a)) + (cos(8a)cos(a) - sin(8a)sin(a)) + 3cos(7a) + 3cos(5a)] / cos(8a)

Simplifying further, we get:

[cos(8a)(cos(3a) + cos(a)) - sin(8a)(sin(3a) + sin(a))] + 3cos(7a) + 3cos(5a) / cos(8a)

Therefore, the simplified expression is:

[cos(8a)(cos(3a) + cos(a)) - sin(8a)(sin(3a) + sin(a))] + 3cos(7a) + 3cos(5a) / cos(8a)