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BITSAT 2011
Exam
BITSAT
Year
2011
Subject
Mathematics
Chapter
Trigonometric Ratios & Identities

BITSAT 2011 · Mathematics · Trigonometric Ratios & Identities

( ( θ)/(1- θ)+( θ)/(1- θ) ) is equal to

(cos⁡θ1−tan⁡θ+sin⁡θ1−cot⁡θ\frac{\cos \theta}{1-\tan \theta}+\frac{\sin \theta}{1-\cot \theta}) is equal to

Options

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

Correct answer

B. (\sin \theta+\cos \theta)

Step-by-step solution

(cos⁡θ1−tan⁡θ+sin⁡θ1−cot⁡θ=cos⁡θ1−sin⁡θcos⁡θ+sin⁡θ1−cos⁡θsin⁡θ=cos⁡2θcos⁡θ−sin⁡θ−sin⁡2θcos⁡θ−sin⁡θ=cos⁡θ+sin⁡θ\begin{aligned} & \frac{\cos \theta}{1-\tan \theta}+\frac{\sin \theta}{1-\cot \theta}=\frac{\cos \theta}{1-\frac{\sin \theta}{\cos \theta}}+\frac{\sin \theta}{1-\frac{\cos \theta}{\sin \theta}}\\ = & \frac{\cos ^2 \theta}{\cos \theta-\sin \theta}-\frac{\sin ^2 \theta}{\cos \theta-\sin \theta}=\cos \theta+\sin \theta \end{aligned}$)
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