Question

Cos 5 a + cos 9 a÷ sin 5a+ sin9a​

Answer 1

Ответ:

решение смотри на фотографии

Answer 2

To simplify the expression (cos(5a) + cos(9a)) / (sin(5a) + sin(9a)), you can use the sum-to-product identities for trigonometric functions. The sum-to-product identities allow you to express the sum of trigonometric functions as a product of trigonometric functions.

Here's how you can simplify the expression:

1. Use the sum-to-product identity for cosine: cos(A) + cos(B) = 2 * cos((A + B) / 2) * cos((A - B) / 2)

2. Use the sum-to-product identity for sine: sin(A) + sin(B) = 2 * sin((A + B) / 2) * cos((A - B) / 2)

Now, apply these identities to your expression:

(cos(5a) + cos(9a)) / (sin(5a) + sin(9a)) = (2 * cos((5a + 9a) / 2) * cos((5a - 9a) / 2)) / (2 * sin((5a + 9a) / 2) * cos((5a - 9a) / 2))

= (cos(7a) * cos(-2a)) / (sin(7a) * cos(-2a))

Now, notice that cos(-2a) is the same as cos(2a) because the cosine function is an even function. Similarly, sin(7a) is the same as sin(-7a) because the sine function is an odd function. Therefore:

= (cos(7a) * cos(2a)) / (sin(-7a) * cos(2a))

Now, cos(2a) cancels out in the numerator and denominator:

= cos(7a) / sin(-7a)

Finally, remember that sin(-x) = -sin(x), so:

= -cos(7a) / sin(7a)

So, the simplified expression is:

• cos(7a) / sin(7a)