Question

3tgx4x-2ctg(пи/2-4x)=1

Answer 1

$3tg4x-2Ctg(\frac{\pi }{2}-4x)=1\\\\3tg4x-2tg4x=1\\\\tg4x=1\\\\4x=arc tg1+\pi n,n\in Z\\\\4x=\frac{\pi }{4} +\pi n,n\in Z\\\\x=\frac{\pi }{16}+\frac{\pi n}{4} ,n\in Z\\\\Otvet:\boxed{\frac{\pi }{16}+\frac{\pi n}{4},n\in Z}$

Answer 2

The equation you've provided seems to involve trigonometric functions. Let's work through it step by step.

The equation is: 3tg(x) - 2ctg(π/2 - 4x) = 1

Here's the breakdown of the equation:

1. tg(x): This is the tangent function.
2. ctg(π/2 - 4x): This is the cotangent function of the angle (π/2 - 4x). The cotangent function is the reciprocal of the tangent function: ctg(θ) = 1 / tg(θ).

First, let's simplify the equation by replacing ctg(π/2 - 4x) with its equivalent in terms of the tangent function:

ctg(π/2 - 4x) = 1 / tg(π/2 - 4x)

Now the equation becomes:

3tg(x) - 2 * (1 / tg(π/2 - 4x)) = 1

Simplify further:

3tg(x) - 2 / tg(π/2 - 4x) = 1

Now, we have the equation in terms of the tangent function. However, solving this equation analytically might be quite complex due to the presence of trigonometric functions. If you have a specific value for 'x' that you're trying to solve for, you can substitute it into the equation and calculate the left-hand side and the right-hand side separately to see if they are equal.

If you're looking for a general solution, you might need to use numerical methods or specialized software to approximate the solutions. Keep in mind that trigonometric equations can sometimes have multiple solutions or no real solutions depending on the equation and the range of values considered for 'x'.