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AP EAMCET · Maths · Trigonometric Ratios & Identities

\(\frac{\tan A}{1-\cot A}+\frac{\cot A}{1-\tan A}=\)

  1. A \(\sec A \operatorname{cosec} A-1\)
  2. B \(\tan A+\cot A\)
  3. C \(\tan A+\cot A+1\)
  4. D \(\sec A+\operatorname{cosec} A+1\)
Verified Solution

Answer & Solution

Correct Answer

(C) \(\tan A+\cot A+1\)

Step-by-step Solution

Detailed explanation

\begin{aligned} & \text {} \frac{\tan A}{1-\cot A}+\frac{\cot A}{1-\tan A}=\frac{\frac{\sin A}{\cos A}}{1-\frac{\cos A}{\sin A}}+\frac{\frac{\cos A}{\sin A}}{1-\frac{\sin A}{\cos A}} \\ & =\frac{\sin ^2 A}{\cos A(\sin A-\cos A)}+\frac{\cos ^2 A}{\sin A(\cos A-\sin A)} \\ &…