cos θ/1−tan θ + sin θ/1−cot θ = ……… A) cos θ – sin θ  B) tan θ – cot θ  C) cos θ – sin θ  D) tan θ + cot θ

Correct option is: C) cos \(\theta\)  + sin  \(\theta\)

\(\frac{cos\theta}{1-tan\theta} + \frac{sin\theta}{1-cot\theta}\)= \(\frac {cos\theta}{\frac {1-sin\theta}{cos\theta}} + \frac {sin\theta}{\frac {1-cos\theta}{sin\theta}}\)

= \(\frac {cos^2\theta}{cos\theta - sin \theta} + \frac {sin^2\theta}{sin\theta - cos\theta}\)

= \(\frac {cos^2\theta}{cos\theta - sin \theta} - \frac {sin^2\theta}{sin\theta - cos\theta}\)

= \(\frac {cos^2\theta - sin^2\theta}{cos\theta - sin \theta}\)

= \(\frac {(cos\theta - sin \theta) (cos\theta + sin \theta)}{cos\theta - sin\theta}\)

= cos \(\theta\) + sin \(\theta\)

Correct option is: A) cos θ – sin θ