Question

3arccos(-1/2)+2arcctg(- корень из 3)-arccos (-1)

Answer 1

Ответ: 8p/3

Объяснение:

=3*2p/3 +2* 5p/6  -p=6p/3 +5p/3 -p=11p/3-p=8p/3

Answer 2

To simplify the expression, let's work on each term one by one:

1. $\arccos\left(-\frac{1}{2}\right)$: The angle whose cosine is $-\frac{1}{2}$ is $\frac{2\pi}{3}$ in the second quadrant. So, $\arccos\left(-\frac{1}{2}\right) = \frac{2\pi}{3}$.

2. $2\arccot\left(-\sqrt{3}\right)$: The cotangent of an angle whose tangent is $-\sqrt{3}$ is $-\frac{1}{\sqrt{3}} = -\frac{\sqrt{3}}{3}$. The angle whose tangent is $-\sqrt{3}$ is $-\frac{\pi}{6}$ (in the fourth quadrant). So, $2\arccot\left(-\sqrt{3}\right) = 2\left(-\frac{\pi}{6}\right) = -\frac{\pi}{3}$.

3. $\arccos(-1)$: The cosine of an angle whose value is -1 is $0$. The angle whose cosine is $0$ is $\frac{\pi}{2}$. So, $\arccos(-1) = \frac{\pi}{2}$.

Now, let's substitute these values back into the expression:

$\frac{2\pi}{3} - \frac{\pi}{3} - \frac{\pi}{2} = \frac{2\pi}{3} - \frac{3\pi}{6} - \frac{3\pi}{6} = \frac{2\pi}{3} - \frac{2\pi}{3} = 0$.

So, the simplified value of the expression is $0$.