AP EAMCET · Maths · Trigonometric Ratios & Identities
If \(\tan A-\tan B=x\) and \(\cot A-\cot B=y\), then \(\cot (A-B)=\)
- A \(\frac{x y}{x+y}\)
- B \(\frac{x y}{x-y}\)
- C \(\frac{x-y}{x y}\)
- D \(\frac{y-x}{x y}\)
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, \(\quad \cot A \cot B=-\frac{y}{x}\)…
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