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NDA 2018
Exam
NDA
Year
2018
Subject
Mathematics
Chapter
Trigonometric Ratios & Identities

NDA 2018 · Mathematics · Trigonometric Ratios & Identities

Suppose A is given. If only one value of ((A)/(2))is possible, then...

Suppose cos⁡A\cos A is given. If only one value of cos⁡(A2)ispossible,thenAmustbe\cos \left(\frac{A}{2}\right)is possible, then A must be

Options

  1. AAn odd multiple of 90∘90^{{}^{\circ}}
  2. BA multiple of 90∘90^{{}^{\circ}}
  3. CAn odd multiple of 180∘180^{{}^{\circ}}
  4. DA multiple of 180∘180^{{}^{\circ}}

Correct answer

C. An odd multiple of 180∘180^{{}^{\circ}}

Step-by-step solution

Given, cos⁡A2\cos \frac{\mathrm{A}}{2} has only one value. We know, cos⁡A=2cos⁡2A2−1⇒2cos⁡2A2=cos⁡A+1⇒cos⁡A2=cos⁡A+12\cos \mathrm{A}=2 \cos ^2 \frac{\mathrm{ A}}{2}-1\Rightarrow 2 \cos ^2 \frac{\mathrm{ A}}{2}=\cos \mathrm{A}+1 \Rightarrow \cos \frac{\mathrm{ A}}{2}=\sqrt{\frac{\cos \mathrm{A}+1}{2}} Since, cos⁡A2\cos \frac{A}{2} is single value, cos⁡A+12=0⇒cos⁡A=−1\frac{\cos A+1}{2}=0\Rightarrow \cos \mathrm{A}=-1 So, A is an odd multiple of 180∘180^{{}^{\circ}}.
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