### Finding the General Solution of the Equation tan^2 x+ 2* (3^1/2) tan x= 1

This article will discuss the general solution of the equation tan^2 x+ 2* (3^1/2) tan x= 1. We will look at the steps involved in finding the solution and provide examples to illustrate the process. We will also provide a glossary of terms and a disclaimer at the end of the article.

Rearrange the equation to ax^2 + bx + c = 0

Solve the equation using the quadratic formula

The general solution is x = tan^-1 (3^1/2) + 2nπ and x = tan^-1 (-3^1/2) + 2nπ, where n is an integer

The equation tan^2 x+ 2* (3^1/2) tan x= 1 is a trigonometric equation. It can be solved by using the quadratic formula. The first step is to rearrange the equation so that it is in the form ax^2 + bx + c = 0. To do this, we need to isolate the tan^2 x term on one side of the equation. We can do this by subtracting 1 from both sides of the equation, giving us tan^2 x+ 2* (3^1/2) tan x - 1 = 0. We can then factorise the equation to get (tan x + 3^1/2)(tan x - 3^1/2) = 0. This equation can then be solved using the quadratic formula, which states that the solutions of the equation are x = tan^-1 (3^1/2) and x = tan^-1 (-3^1/2).

The general solution of the equation tan^2 x+ 2* (3^1/2) tan x= 1 is therefore x = tan^-1 (3^1/2) + 2nπ and x = tan^-1 (-3^1/2) + 2nπ, where n is an integer. This means that the solution can be any value of x that satisfies the equation, plus any multiple of 2π. For example, if x = tan^-1 (3^1/2), then the general solution would be x = tan^-1 (3^1/2) + 2nπ, where n is an integer.

Good to know:

**Trigonometric equation:**an equation involving trigonometric functions such as sine, cosine, and tangent**Quadratic formula:**a formula used to solve quadratic equations

In conclusion, the general solution of the equation tan^2 x+ 2* (3^1/2) tan x= 1 is x = tan^-1 (3^1/2) + 2nπ and x = tan^-1 (-3^1/2) + 2nπ, where n is an integer. This means that the solution can be any value of x that satisfies the equation, plus any multiple of 2π.

The information provided in this article is for educational purposes only and should not be used as a substitute for professional advice.