SOLUTION: Prove the identity: {{{cot^""(A)}}}{{{""-""}}}{{{tan^""(A)}}}{{{""=""}}}{{{2cot^""(2A)}}}

Algebra ->  Trigonometry-basics -> SOLUTION: Prove the identity: {{{cot^""(A)}}}{{{""-""}}}{{{tan^""(A)}}}{{{""=""}}}{{{2cot^""(2A)}}}      Log On


   

Question 1056804: Prove the identity:
cot%5E%22%22%28A%29%22%22-%22%22tan%5E%22%22%28A%29%22%22=%22%222cot%5E%22%22%282A%29
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!

cot%5E%22%22%28A%29%22%22-%22%22tan%5E%22%22%28A%29%22%22=%22%222cot%5E%22%22%282A%29

Work with the right side:

2cot%5E%22%22%282A%29

2%5E%22%22%2Ftan%5E%22%22%282A%29

2%22%F7%22tan%5E%22%22%282A%29

Use formula for tan(2A)

2%22%F7%22%28%282tan%5E%22%22%28A%29%29%2F%281-tan%5E2%28A%29%29%29

Invert the second and multiply:

2%22%D7%22%28%281-tan%5E2%28A%29%29%2F2tan%5E%22%22%28A%29%29%29

cross%282%29%22%D7%22%28%281-tan%5E2%28A%29%29%2Fcross%282%29tan%5E%22%22%28A%29%29%29

%281-tan%5E2%28A%29%29%2Ftan%5E%22%22%28A%29%29

Break into two fractions:

1%5E%22%22%2Ftan%5E%22%22%28A%29%22%22-%22%22tan%5E2%28A%29%2Ftan%5E%22%22%28A%29

cot%5E%22%22%28A%29%22%22-%22%22tan%5Ecross%282%29%28A%29%2Fcross%28tan%5E%22%22%28A%29%29

cot%5E%22%22%28A%29%22%22-%22%22tan%5E%22%22%28A%29

Edwin