ExamBro
ExamBro
TS EAMCET · Maths · Trigonometric Ratios & Identities

If \(\tan A+\tan B+\cot A+\cot B=\tan A \tan B-\cot A \cot B\) and \(0^{\circ} \lt A+B \lt 270^{\circ}\), then \(A+B=\)

  1. A \(45^{\circ}\)
  2. B \(135^{\circ}\)
  3. C \(150^{\circ}\)
  4. D \(225^{\circ}\)
Verified Solution

Answer & Solution

Correct Answer

(B) \(135^{\circ}\)

Step-by-step Solution

Detailed explanation

\begin{aligned} & \tan A+\tan B+\cot A+\cot B \\ & =\tan A \tan B-\cot A \cot B \\ & \Rightarrow \tan (A+B)(1-\tan A \tan B)+\frac{\cot A \cot B-1}{\cot (A+B)} \\ & =\tan A \tan B-\cot A \cot B \\ & \Rightarrow \tan (A+B)(1-\tan A \tan B+\cot A \cot B-1) \\ & \quad=(\tan A \tan…