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NDA 2018
Exam
NDA
Year
2018
Subject
Mathematics
Chapter
Trigonometric Equations

NDA 2018 · Mathematics · Trigonometric Equations

A is an angle in the fourth quadrant. If satisfies the...

AA is an angle in the fourth quadrant. If satisfies the trigonometric equation 3(3−tan⁡2A−cot⁡A)2=13\left(3-\tan ^2 \mathrm{ A}-\cot \mathrm{A}\right)^2=1. Which one of the following is a value of AA ?

Options

  1. A300∘300^{{}^{\circ}}
  2. B315∘315^{{}^{\circ}}
  3. C330∘330^{{}^{\circ}}
  4. D345∘345^{{}^{\circ}}

Correct answer

A. 300∘300^{{}^{\circ}}

Step-by-step solution

Checking through options 300∘=−60∘300^{{}^{\circ}}=-60^{{}^{\circ}} So, 3[3−tan⁡2(−60∘)−cot⁡(−60∘)]2=3[3−3+13]2=3×13=13\left[3-\tan ^2\left(-60^{{}^{\circ}}\right)-\cot \left(-60^{{}^{\circ}}\right)\right]^2=3\left[3-3+\frac{1}{\sqrt{3}}\right]^2=3 \times \frac{1}{3}=1
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