SOLUTION: Hello,   I apologize that I base a new article, but I need to deal with this example. I did not know council. tan(2x)cot(x) = cot(2x)tan(x) <a rel=nofollow HREF="http://w

Algebra ->  Trigonometry-basics -> SOLUTION: Hello,   I apologize that I base a new article, but I need to deal with this example. I did not know council. tan(2x)cot(x) = cot(2x)tan(x) <a rel=nofollow HREF="http://w      Log On


   



Question 969275: Hello,
  I apologize that I base a new article, but I need to deal with this example. I did not know council.
tan(2x)cot(x) = cot(2x)tan(x)


thank you

Answer by Edwin McCravy(20065) About Me  (Show Source):
You can put this solution on YOUR website!
tan%282x%29cot%28x%29%22%22=%22%22cot%282x%29tan%28x%29

We must rule out all values where some of those are undefined,

x%3C%3En%2Api%2F4, or all multiples of 45°

tan%282x%29%2Ftan%28x%29%22%22=%22%22tan%28x%29%2Ftan%282x%29

tan%5E2%282x%29%22=%22%22tan%5E2%28x%29

tan%282x%29%22%22=%22%22%22%22+%2B-+tan%28x%29

%282tan%28x%29%29%2F%281-tan%5E2%28x%29%29%22%22=%22%22%22%22+%2B-+tan%28x%29

2tan%28x%29%22%22=%22%22%22%22+%2B-+tan%28x%29%281-tan%5E2%28x%29%5E%22%22%29

We can divide both sides by tan(x) since tan(x) cannot be 0.

2%22%22=%22%22%22%22+%2B-+%281-tan%5E2%28x%29%5E%22%22%29

Using the + sign,

2%22%22=%22%22%22%22%2B%281-tan%5E2%28x%29%5E%22%22%29
2%22%22=%22%221-tan%5E2%28x%29
tan%5E2%28x%29%22%22=%22%22-1

This would give an imaginary answer.

Using the - sign,

2%22%22=%22%22-%281-tan%5E2%28x%29%5E%22%22%29
2%22%22=%22%22-1%2Btan%5E2%28x%29
3%22%22=%22%22tan%5E2%28x%29
%22%22+%2B-+sqrt%283%29%22%22=%22%22tan%28x%29

x%22%22=%22%22pi%2F3%2Bn%2Api,2pi%2F3%2Bn%2Api
x%22%22=%22%22expr%28pi%2F3%29%281%2B3n%29,expr%28pi%2F3%29%282%2B3n%29

or in degrees:

x%22%22=%22%22%2260%B0%22%2B%22180%B0%22n, %22120%B0%22%2B%22180%B0%22n
x%22%22=%22%22%2260%B0%22%281%2B3n%29, %2260%B0%22%282%2B3n%29

Edwin