Simple trigonometric problem: If tan(x) - cot(x) = 2√3, what is their sum?
- Thread starter DarkRose
- Start date
- Joined
- Feb 4, 2004
- Messages
- 16,582
What is whose sum?
What is whose sum?
The sum of tan(x)+cot(x)
D
Deleted member 4993
Guest
What are your thoughts?
Please share your work with us ...even if you know it is wrong.
If you are stuck at the beginning tell us and we'll start with the definitions.
You need to read the rules of this forum. Please read the post titled "Read before Posting" at the following URL:
http://www.freemathhelp.com/forum/announcement.php?f=33
- Joined
- Feb 4, 2004
- Messages
- 16,582
Okay. So you have this:
. . . . .\(\displaystyle \tan(x)\, -\, \cot(x)\, =\, 2\, \sqrt{\strut 3\,}\)
You know that:
. . . . .\(\displaystyle \cot(x)\, =\, \dfrac{1}{\tan(x)}\)
Using this identity, you can get to here:
. . . . .\(\displaystyle \tan(x)\, -\, \dfrac{1}{\tan(x)}\, =\, 2\, \sqrt{\strut 3\,}\)
Combine the two terms (the tangent and the tangent-fraction) into one:
. . . . .\(\displaystyle \dfrac{\tan^2(x)\, -\, 1}{\tan(x)}\, =\, 2\, \sqrt{\strut 3\,}\)
Multiply through and move everything over onto one side of the "equals" sign. You'll get a quadratic in tangent. Solve for the values of tan(x), and choose the correct solution for the specified interval. Then find the value for cot(x). Then sum.
If you get stuck, please reply showing your thoughts and efforts so far. Thank you!