Question

Tg(2arccos(5/√26)-arcsin(12/13))=

Answer 1

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Answer 2

To find the value of the given trigonometric expression, we can start by using trigonometric identities to simplify it.

Let's denote: A = 2arccos(5/√26) and B = arcsin(12/13).

We know the following trigonometric identities:

1. arccos(x) + arcsin(x) = π/2, for all valid x values.
2. arccos(x) + arcsin(y) = π/2, if x^2 + y^2 = 1.

Using the first identity, we can rewrite A and B as: A = arccos(5/√26) + arccos(5/√26) B = arcsin(12/13)

Now, let's focus on finding the value of A first. We will use the second identity to rewrite the two arccosine terms into a single term: arccos(5/√26) + arccos(5/√26) = arccos(5/√26) + arcsin(√(1 - (5/√26)^2)) = arccos(5/√26) + arcsin(√((26 - 5^2)/26)) = arccos(5/√26) + arcsin(√(1/26)) = arccos(5/√26) + arcsin(1/√26)

Now we can rewrite A as: A = arccos(5/√26) + arcsin(1/√26)

Now, we have A and B in the same form, and we can use the first identity to combine them: Tg(A - B) = Tg(arccos(5/√26) + arcsin(1/√26) - arcsin(12/13))

Unfortunately, we can't simplify this expression further without knowing the specific values of the angles involved. So, the final answer will remain in this form:

Tg(2arccos(5/√26) - arcsin(12/13)) = Tg(arccos(5/√26) + arcsin(1/√26) - arcsin(12/13))

If you have specific values for the angles involved (e.g., the values of arccos(5/√26), arcsin(1/√26), and arcsin(12/13)), then you can substitute those values into the expression to find the numerical result.