# What is the answer to tan^2 x-sec x-1 = 0 in 0,2\pi).

## Question:

What is the answer to {eq}tan^2 x-sec x-1 = 0 {/eq} in [ {eq}0,2\pi {/eq}).

## Solving Trigonometric Equations:

The solution of an equation that includes trigonometric functions in variable {eq}x {/eq}, where {eq}x {/eq} lies in {eq}\in \left[0,2\pi\right), {/eq} is called the principal solution. If the solution contains the integer {eq}n {/eq} in it, it gives all the solutions and is called the general solution.

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Given:

{eq}\tan ^2 x - \sec x -1 =0\\ (\sec^2 x -1) - \sec x - 1=0\\ \sec^2 x - \sec x - 2=0\\ \sec^2 x - 2\sec x +\sec x- 2=0\\ (\sec x -...

Solving Trigonometric Equations with Infinite Solutions

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Chapter 22 / Lesson 5
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In trigonometry, equations have an infinite number of solutions. In this lesson, review the period, explore sine, cosine, and tangent, and work through examples to understand the different ways that trigonometric equations can be solved.