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NDA 2021
Exam
NDA
Year
2021
Subject
Mathematics
Chapter
Trigonometric Ratios & Identities

NDA 2021 · Mathematics · Trigonometric Ratios & Identities

What is (1+ ^2 θ)/(1+ ^2 θ)- ((1- θ)/(1- θ))^2 equal to?

What is \frac{1+\tan ^2 \theta}{1+\cot ^2 \theta}-(1−tan⁡θ1−cot⁡θ)2\left(\frac{1-\tan \theta}{1-\cot \theta}\right)^2 equal to?

Options

  1. A00
  2. B11
  3. C2tan⁡θ2 \tan \theta
  4. D2cot⁡θ2 \cot \theta

Correct answer

A. 00

Step-by-step solution

1+tan⁡2θ1+cot⁡2θ−(1−tan⁡θ1−cot⁡θ)2\frac{1+\tan ^2 \theta}{1+\cot ^2 \theta}-\left(\frac{1-\tan \theta}{1-\cot \theta}\right)^2=1+tan⁡2θtan⁡2θ+1tan⁡2θ−(1−tan⁡θtan⁡θ−1tan⁡θ)2&=tan⁡2θ−(−tan⁡θ)2=0.\begin{aligned}& =\frac{1+\tan ^2 \theta}{\frac{\tan ^2 \theta+1}{\tan ^2 \theta}}-\left(\frac{1-\tan \theta}{\frac{\tan \theta-1}{\tan \theta}}\right)^2 \& =\tan ^2 \theta-(-\tan \theta)^2=0. \end{aligned}$$
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