Question

Вычислить tgA если известно что cos 2a = -5/13 aЭ [П, 3П/2] Помогайте пж

Answer 1

Применена универсальная подстановка

Answer 2

Calculating tgA given cos 2A = -5/13

To calculate the value of tgA when cos 2A = -5/13, we can use the double angle identity for tangent, which states that:

tan(2A) = (2 * tan(A)) / (1 - tan^2(A))

We can use the given value of cos 2A to find sin 2A and then use the double angle identities to find the value of tan A.

First, let's find sin 2A using the given value of cos 2A.

Given: cos 2A = -5/13

Using the identity: cos(2A) = 1 - 2sin^2(A)

We can solve for sin 2A: sin^2(2A) = (1 - cos(2A)) / 2

sin^2(2A) = (1 - (-5/13)) / 2

sin^2(2A) = (1 + 5/13) / 2

sin^2(2A) = (18/13) / 2

sin^2(2A) = 9/13

Now, we can find sin 2A: sin(2A) = ±√(9/13)

Since sin is positive in the second and fourth quadrants, we take the positive square root: sin(2A) = √(9/13) = 3/√13

Now that we have sin 2A, we can use the double angle identity for tangent to find the value of tan A.

Using the identity: tan(2A) = (2 * tan(A)) / (1 - tan^2(A))

We can solve for tan A: tan(2A) = (2 * tan(A)) / (1 - tan^2(A))

Substitute sin 2A and cos 2A: (3/√13) / (-5/13) = (2 * tan(A)) / (1 - tan^2(A))

Solving for tan A: tan(A) = ((3/√13) / (-5/13)) / (2 / (1 - tan^2(A)))

This gives us the value of tgA in terms of tan^2(A), and we can solve for tan^2(A) using this equation.

Let's proceed with the calculation.