Question

(cos5a+5cos3a+10cosa)/cos^5a

Answer 1

Ответ:

16

Пошаговое объяснение:

$\dfrac{cos5a+5cos3a+10cosa}{cos^5a}$

Рассмотрим числитель дроби:

$cos5a+5cos3a+10cosa=16cos^5a-20cos^3a+5cosa+20cos^3a-15cosa+\\+10cosa=16cos^5a$

Тогда дробь примет вид:

$\dfrac{16cos^5a}{cos^5a}=16$

Задание выполнено!

Answer 2

To simplify the given expression, let's break it down step by step:

Expression: (cos^5a + 5cos^3a + 10cosa) / cos^5a

Step 1: Factor out the common term "cosa" from the numerator. Expression becomes: cosa * (cos^4a + 5cos^2a + 10) / cos^5a

Step 2: Divide each term in the numerator by cos^5a. Expression becomes: cosa * (cos^4a / cos^5a + 5cos^2a / cos^5a + 10 / cos^5a)

Step 3: Simplify the fractions in the numerator. cos^4a / cos^5a simplifies to cos^(-1)a, and cos^2a / cos^5a simplifies to cos^(-3)a. Expression becomes: cosa * (cos^(-1)a + 5cos^(-3)a + 10 / cos^5a)

So, the simplified expression is: cosa * (cos^(-1)a + 5cos^(-3)a + 10 / cos^5a)

Please note that "cos^(-1)a" refers to the reciprocal of cos(a), and "cos^(-3)a" refers to the cube of the reciprocal of cos(a).