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AP EAMCET · Maths · Trigonometric Ratios & Identities

If \(A B C\) is not a right angled triangle and \(\sin \left(\frac{\pi}{4}-A\right) \sin \left(\frac{\pi}{4}-B\right)=-\frac{1}{2 \sqrt{2}} \operatorname{cosec}\left(\frac{\pi}{4}-C\right)\), then \(\tan A \tan B+\tan B \tan C+\tan C \tan A=\)

  1. A \(\cot A+\cot B+\cot C\)
  2. B \(\tan A+\tan B+\tan C\)
  3. C \(\frac{1}{\tan A+\tan B+\tan C}\)
  4. D \(\frac{1}{\cot A+\cot B+\cot C}\)
Verified Solution

Answer & Solution

Correct Answer

(B) \(\tan A+\tan B+\tan C\)

Step-by-step Solution

Detailed explanation

Given, \(A+B+C=\pi\) We know that, \(\cos (A+B+C)=\cos A \cos B \cos C(l-\tan A \tan B\) \(-\tan B \tan C-\tan A \tan C)\) and \(\tan A+\tan B+\tan C=\tan A \tan B \tan C\) Now,…