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 \(A+B=\)
- A \(45^{\circ}\)
- B \(135^{\circ}\)
- C \(150^{\circ}\)
- D \(225^{\circ}\)
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…
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