Question

2cos2альфа :sin2альфа

Answer 1

Ответ:

$2ctg2a$

Пошаговое объяснение:

$\frac{2cos2a}{sin2a}=2ctg2a$

Answer 2

To simplify the expression 2cos(2α) : sin(2α), we can use trigonometric identities.

Recall the double-angle identities:

cos(2α) = cos²(α) - sin²(α) sin(2α) = 2sin(α)cos(α)

Let's substitute these values into our expression:

2cos(2α) : sin(2α) = 2(cos²(α) - sin²(α)) : 2sin(α)cos(α)

Cancel out the common factor of 2:

cos²(α) - sin²(α) : sin(α)cos(α)

Now, we can simplify further using the Pythagorean identity:

cos²(α) = 1 - sin²(α)

Substitute this into the expression:

(1 - sin²(α)) - sin²(α) : sin(α)cos(α)

Simplify:

1 - 2sin²(α) : sin(α)cos(α)

Now, we can factor out sin(α) from the numerator:

sin(α)(1 - 2sin(α)) : sin(α)cos(α)

Cancel out the common factor of sin(α):

1 - 2sin(α) : cos(α)

This is the simplified form of the expression 2cos(2α) : sin(2α).