How Do You Solve the Equation tan(x) + sec(x) = 1?

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In summary, trigonometric solutions involve using trigonometric functions to find unknown values in a right triangle. The equation tanx+secx=1 is a trigonometric identity that is used to find the value of x in a right triangle when the tangent and secant of that angle add up to one. To solve this equation, you can use algebraic manipulation and trigonometric identities, and there are two special cases to consider. You can check your solution by plugging it back into the equation or graphing it on a calculator.
  • #1
jrjack
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Homework Statement


tanx+secx=1


Homework Equations





The Attempt at a Solution


tanx+secx=1
tanx=1-secx then square both sides?
[tex]\tan^2 x= 1-2\sec x+\sec^2 x[/tex][tex]\sec^2 x-1=1-2\sec x+\sec^2 x[/tex][tex]2-2\sec x=0[/tex][tex]\sec x=0[/tex] No Solution
 
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  • #2
2 -2sec(x)=0 gives sec(x)=1, not 0.
 
  • #3
Thanks, I was trying to factor out a 2 when,
I should have subtracted 2 then divided by 2, getting sec(x)=1
 

Related to How Do You Solve the Equation tan(x) + sec(x) = 1?

1. What does "Trig solution" mean?

In mathematics, trigonometric solutions refer to finding the values of unknown angles or sides in a right triangle using trigonometric functions such as sine, cosine, and tangent.

2. What is the equation tanx+secx=1 used for?

This equation is used to find the value of the angle x in a right triangle when the tangent and secant of that angle add up to one. It is also known as a trigonometric identity.

3. How do you solve tanx+secx=1?

To solve this equation, you can use algebraic manipulation and trigonometric identities to rewrite the equation in terms of a single trigonometric function. Then, you can use inverse trigonometric functions to find the value of x.

4. Are there any special cases when solving tanx+secx=1?

Yes, there are two special cases to consider when solving this equation. The first is when x=0, in which case the equation is true for all values of x. The second is when x=π/2, in which case the equation is undefined.

5. How can I check my solution for tanx+secx=1?

You can check your solution by plugging it back into the original equation. If the equation holds true, then your solution is correct. Additionally, you can also graph the equation and your solution on a graphing calculator to visually confirm the solution.

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