Question

Вычислить: tg(arctg(корень3)+arccos1/2) Ответ должен быть - корень3

Answer 1

$tg(arctg(\sqrt3)+arccos(1/2))= tg(\pi/3+\pi/3)=tg(2\pi/3)=-\sqrt3$

Answer 2

Calculating tg(arctg(√3) + arccos(1/2))

To calculate the value of tg(arctg(√3) + arccos(1/2)), we can use trigonometric identities and properties to simplify the expression and find the result.

First, let's break down the steps to solve this expression:

1. Identify the Values: - arctg(√3) is the angle whose tangent is √3. - arccos(1/2) is the angle whose cosine is 1/2.

2. Use Trigonometric Identities: - We can use the properties of trigonometric functions to simplify the expression and find the value of tg(arctg(√3) + arccos(1/2)).

3. Calculate the Result: - By applying the appropriate trigonometric identities, we can find the value of tg(arctg(√3) + arccos(1/2)).

Let's proceed with the calculation.

Solution:

The expression tg(arctg(√3) + arccos(1/2)) can be simplified using trigonometric identities. We'll start by finding the values of arctg(√3) and arccos(1/2).

1. arctg(√3) is the angle whose tangent is √3. - This means that tg(arctg(√3)) = √3.

2. arccos(1/2) is the angle whose cosine is 1/2. - This means that cos(arccos(1/2)) = 1/2.

Now, we can use the properties of trigonometric functions to simplify the expression:

tg(arctg(√3) + arccos(1/2)) = tg(arctg(√3)) + tg(arccos(1/2)) = √3 + tg(arccos(1/2))

Using the trigonometric identity tg(arccos(x)) = √(1 - x^2), where -1 < x < 1, we can find tg(arccos(1/2)):

tg(arccos(1/2)) = √(1 - (1/2)^2) = √(1 - 1/4) = √(3/4) = √3/2

Therefore, tg(arctg(√3) + arccos(1/2)) = √3 + √3/2 = √3 + (1/2)√3 = (1 + 1/2)√3 = (3/2)√3 = √3

So, the value of tg(arctg(√3) + arccos(1/2)) is √3.