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COMEDK · Maths · 8. Trigonometric Ratios & Identities

What is \(\dfrac{\cos \theta}{1-\tan \theta}+\dfrac{\sin \theta}{1-\cot \theta}\) equal to?

  1. A \(\sin \theta-\cos \theta\)
  2. B \(2 \sin \theta\)
  3. C \(\sin \theta+\cos \theta\)
  4. D \(2 \cos \theta\)
Verified Solution

Answer & Solution

Correct Answer

(C) \(\sin \theta+\cos \theta\)

Step-by-step Solution

Detailed explanation

The given expression is \(E = \dfrac{\cos \theta}{1 - \tan \theta} + \dfrac{\sin \theta}{1 - \cot \theta}\). Substituting \(\tan \theta = \dfrac{\sin \theta}{\cos \theta}\) and \(\cot \theta = \dfrac{\cos \theta}{\sin \theta}\), we get:…