solve tan2(x+41 degrees) in real number fo degrees

To solve the equation tan(2(x+41°)), where x represents an angle in degrees, we need to find the values of x for which the tangent of twice that angle is a real number.

First, we need to understand the properties of the tangent function. The tangent of an angle is defined as the ratio of the opposite side to the adjacent side in a right triangle. The tangent function has periodicity of 180°, meaning that the tangent of an angle repeats itself every 180°.

Now, let's solve the equation.

tan(2(x+41°)) = tan(2x+82°)

We want to find values of x for which tan(2x+82°) is a real number. A real number is any number which is not imaginary (complex).

In order to find these values, we can solve the equation:

2x + 82° = n*180° + m° (where n = any integer, and m = the angle in degrees for which tan(m) is defined)

We subtract 82° from both sides:

2x = n*180° + m° - 82°

Divide both sides by 2:

x = (n*180° + m° - 82°) / 2

By substituting different values for n, we can find the values of x for which the tangent function is defined. Keep in mind that the tangent function is not defined for angles that are odd multiples of 90° (e.g., 90°, 270°, etc.), since the tangent becomes undefined at those angles.

For example, let's substitute n = 0:

x = (0*180° + m° - 82°) / 2
x = (m° - 82°) / 2

So, for each value of m that satisfies this equation, we can find a corresponding value of x. The resulting values of x will be real numbers for which tan(2(x+41°)) is defined.