Question

Ctg(p/3-1/4x)=5/12 плиз

Answer 1

Х=-4arcctg (5/12)+4п/3+4пК,где К принадлежит целым числам.
Надеюсь поймешь)

Answer 2

To solve the trigonometric equation $\cot\left(\frac{p}{3} - \frac{1}{4}x\right) = \frac{5}{12}$, we need to find the value of $x$.

Step 1: Rewrite the cotangent in terms of the tangent function. The cotangent function is the reciprocal of the tangent function: $\cot(\theta) = \frac{1}{\tan(\theta)}$. So, we can rewrite the equation as:

$\frac{1}{\tan\left(\frac{p}{3} - \frac{1}{4}x\right)} = \frac{5}{12}$.

Step 2: Isolate the tangent function. To do that, take the reciprocal of both sides:

$\tan\left(\frac{p}{3} - \frac{1}{4}x\right) = \frac{12}{5}$.

Step 3: Find the angle $\left(\frac{p}{3} - \frac{1}{4}x\right)$. Now, we can find the angle $\left(\frac{p}{3} - \frac{1}{4}x\right)$ using the inverse tangent function (also known as arctan):

$\frac{p}{3} - \frac{1}{4}x = \arctan\left(\frac{12}{5}\right)$.

Step 4: Solve for $x$. To isolate $x$, we need to get rid of the term with $\frac{p}{3}$ on the left side. So, we'll subtract $\frac{p}{3}$ from both sides:

$-\frac{1}{4}x = \arctan\left(\frac{12}{5}\right) - \frac{p}{3}$.

Finally, solve for $x$ by multiplying both sides by $-4$:

$x = -4 \left( \arctan\left(\frac{12}{5}\right) - \frac{p}{3} \right)$.

And that's the solution for $x$ in terms of $p$.