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TS EAMCET · Maths · Trigonometric Ratios & Identities

If \(0 \leq \mathrm{A}, \mathrm{B} \leq \frac{\pi}{4}\) and \(\cot \mathrm{A}+\cot \mathrm{B}+\tan \mathrm{A}+\tan \mathrm{B}=\cot \mathrm{A} \cot \mathrm{B}-\tan \mathrm{A} \tan \mathrm{B}\) then \(\sin (\mathrm{A}+\mathrm{B})=\)

  1. A \(0\)
  2. B \(\frac{1}{2}\)
  3. C \(\frac{1}{\sqrt{2}}\)
  4. D \(\frac{\sqrt{3}}{2}\)
Verified Solution

Answer & Solution

Correct Answer

(C) \(\frac{1}{\sqrt{2}}\)

Step-by-step Solution

Detailed explanation

\( \frac{1}{\tan A} + \frac{1}{\tan B} + \tan A + \tan B = \frac{1}{\tan A \tan B} - \tan A \tan B \) \( \tan B + \tan A + \tan^2 A \tan B + \tan A \tan^2 B = 1 - \tan^2 A \tan^2 B \) \( (\tan A + \tan B) + \tan A \tan B (\tan A + \tan B) = 1 - (\tan A \tan B)^2 \)…