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AP EAMCET · Maths · Trigonometric Ratios & Identities

If \(\tan A+\tan B=x\) and \(\cot A+\cot B=y\), then \(\tan (\mathrm{A}+\mathrm{B})=\)

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

Answer & Solution

Correct Answer

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

Step-by-step Solution

Detailed explanation

Given, \(\cot A+\cot B=y\) \(\begin{aligned} & \Rightarrow \frac{\tan A+\tan B}{\tan A \tan B}=y \\ & \Rightarrow \tan A-\tan B=\frac{x}{y} \end{aligned}\) Now, \(\tan (A+B)=\frac{\tan A+\tan B}{1-\tan A \cdot \tan B}\) \(=\frac{x}{1-\frac{x}{y}}=\frac{x y}{y-x}\)