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COMEDK · Maths · 8. Trigonometric Ratios & Identities

The expression \(\dfrac{\tan A}{1-\cot A}+\dfrac{\cot A}{1-\tan A}\) can be written as

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

Answer & Solution

Correct Answer

(B) \(\sec A \operatorname{cosec} A+1\)

Step-by-step Solution

Detailed explanation

Let the expression be \(E = \dfrac{\tan A}{1-\cot A} + \dfrac{\cot A}{1-\tan A}\). Substituting \(\cot A = \dfrac{1}{\tan A}\) into the expression: \(E = \dfrac{\tan A}{1-\dfrac{1}{\tan A}} + \dfrac{\dfrac{1}{\tan A}}{1-\tan A}\)…