Question

F(x)=tg(П/4-x)и её значение при x=-3/4П​

Answer 1

Ответ:

0.

Объяснение:

Если Вы просите найти значение функции f(x) = tg(π/4-x) в точкe х = - 3π/4, то решение следующее:

f(x) = tg(π/4-x),

если х = - 3π/4, то

f(-3π/4) = tg(π/4-(-3π/4)) = tgπ = 0.

Answer 2

To find the value of the function $F(x) = \tan\left(\frac{\pi}{4}-x\right)$ at $x = -\frac{3}{4}\pi$, we substitute the value of $x$ into the function:

$F\left(-\frac{3}{4}\pi\right) = \tan\left(\frac{\pi}{4} - \left(-\frac{3}{4}\pi\right)\right)$

Simplifying the expression inside the tangent function:

$= \tan\left(\frac{\pi}{4} + \frac{3}{4}\pi\right)$

Now, we can simplify the argument of the tangent function using the trigonometric identity $\tan(\alpha + \beta) = \frac{{\tan(\alpha) + \tan(\beta)}}{{1 - \tan(\alpha)\tan(\beta)}}$:

$= \frac{{\tan\left(\frac{\pi}{4}\right) + \tan\left(\frac{3}{4}\pi\right)}}{{1 - \tan\left(\frac{\pi}{4}\right)\tan\left(\frac{3}{4}\pi\right)}}$

Using the values of tangent function for $\frac{\pi}{4}$ and $\frac{3}{4}\pi$:

$= \frac{{1 + \tan\left(\frac{3}{4}\pi\right)}}{{1 - 1 \cdot \tan\left(\frac{3}{4}\pi\right)}}$

Since $\tan\left(\frac{3}{4}\pi\right) = \tan\left(\frac{\pi}{4} + \frac{1}{2}\pi\right) = -1$, the expression becomes:

$= \frac{{1 + (-1)}}{{1 - (-1)}} = \frac{0}{2} = 0$

Therefore, $F\left(-\frac{3}{4}\pi\right) = 0$ when evaluated at $x = -\frac{3}{4}\pi$.