Help with solving this equation

  • Thread starter donjt81
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In summary, solving an equation involves finding the value of the variable that makes the equation true. The steps to solve an equation may vary, but generally include simplifying both sides, isolating the variable, and checking the solution. For example, to solve 2x + 5 = 15, we can subtract 5 from both sides and divide by 2. If the equation has fractions or decimals, you can eliminate them by multiplying by the LCM of the denominators. To check the solution, plug it back in or graph it.
  • #1
donjt81
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Hi guys

I was solving a problem and I am stuck at solving this equation.

(sec x)^2 (tan x)^2 = 2
since we know that (sec x)^2 = 1 + (tan x)^2

[1 + (tan x)^2][(tan x)^2] = 2
(tan x)^2 + (tan x)^4 - 2 = 0

now what do i do...

thanks in advance.
 
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  • #2
Substitute "u = tan x" to get a quadratic.
 
  • #3


Hello,

Thank you for reaching out for assistance with your equation. It looks like you have made a good start by using the identity (sec x)^2 = 1 + (tan x)^2. The next step would be to substitute this into your original equation:

(1 + (tan x)^2)(tan x)^2 = 2

Now, you can expand out the brackets and rearrange the terms to get a quadratic equation in terms of (tan x)^2:

(tan x)^4 + (tan x)^2 - 2 = 0

This can be solved using the quadratic formula, where a = 1, b = 1, and c = -2. You should get two solutions for (tan x)^2, which you can then take the square root of to find the values of tan x. From there, you can find the values of x by using the inverse tangent function.

I hope this helps you continue solving your equation. Remember to always check your solutions to make sure they satisfy the original equation. Good luck!
 

Related to Help with solving this equation

1. How do I solve this equation?

Solving an equation involves finding the value of the variable that makes the equation true. To solve an equation, you can use various methods such as substitution, elimination, or graphing.

2. What are the steps to solve an equation?

The steps to solve an equation may vary depending on the type of equation. Generally, the steps involve simplifying both sides of the equation, isolating the variable, and checking your solution by plugging it back into the original equation.

3. Can you show me an example of solving an equation?

Yes, for example, to solve the equation 2x + 5 = 15, we can subtract 5 from both sides to get 2x = 10. Then, we divide both sides by 2 to get x = 5. To check our solution, we plug in x = 5 back into the original equation and see if it makes the equation true.

4. What if the equation has fractions or decimals?

If the equation has fractions or decimals, you can eliminate them by multiplying both sides of the equation by the least common multiple (LCM) of all the denominators. This will result in an equation with whole numbers that can be solved using the same steps as a regular equation.

5. How can I check if my solution is correct?

You can check your solution by plugging it back into the original equation and seeing if it makes the equation true. If it does, then your solution is correct. You can also graph the equation and your solution to visually confirm it.

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