ExamBro
ExamBro
AP EAMCET · Maths · Trigonometric Ratios & Identities

If \(\tan A-\tan B=x\) and \(\cot A-\cot B=y\), then \(\cot (A-B)=\)

  1. A \(\frac{x y}{x+y}\)
  2. B \(\frac{x y}{x-y}\)
  3. C \(\frac{x-y}{x y}\)
  4. D \(\frac{y-x}{x y}\)
Verified Solution

Answer & Solution

Correct Answer

(D) \(\frac{y-x}{x y}\)

Step-by-step Solution

Detailed explanation

Since, \(\tan A-\tan B=x\) \(\Rightarrow \frac{1}{\cot A}-\frac{1}{\cot B}=x \Rightarrow \frac{\cot B-\cot A}{\cot A \cot B}=x\) \(\because \quad \cot A-\cot B=y\) (given) So, \(\quad \cot A \cot B=-\frac{y}{x}\)…