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NDA 2019
Exam
NDA
Year
2019
Subject
Mathematics
Chapter
Trigonometric Ratios & Identities

NDA 2019 · Mathematics · Trigonometric Ratios & Identities

Consider the following statements: 1. θ+ θ can never be equal to...

Consider the following statements: 1. cos⁡θ+sec⁡θ\cos \theta+\sec \theta can never be equal to 1.5. 2. tan⁡θ+cot⁡θ\tan \theta+\cot \theta can never be less than 2. Which of the above statements is/are correct?

Options

  1. A1 only
  2. B2 only
  3. CBoth 1 and 2
  4. DNeither 1 nor 2

Correct answer

A. 1 only

Step-by-step solution

 (i) cos⁡θ+sec⁡θ=32⇒1+cos⁡2θcos⁡θ=32⇒2cos⁡2θ−3cos⁡θ+2=0\begin{aligned} & \text{ (i) } \cos \theta+\sec \theta=\frac{3}{2} \\ & \Rightarrow \frac{1+\cos ^2 \theta}{\cos \theta}=\frac{3}{2} \\ & \Rightarrow 2 \cos ^2 \theta-3 \cos \theta+2=0 \end{aligned} here discriminant is negative ∴\therefore No real roots ∴\therefore No solution. (ii) In second quadrant both tan⁡θandcot⁡θ\tan \theta and \cot \theta are negative ∴\therefore In second quadrant value is less than 2 . So only statement 1 is true.
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