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NDA 2022
Exam
NDA
Year
2022
Subject
Mathematics
Chapter
Trigonometric Ratios & Identities

NDA 2022 · Mathematics · Trigonometric Ratios & Identities

What is the value of (2 n π+(5 π)/(6)) (2 n π-(5 π)/(6)), where n ∈...

What is the value of sin⁡(2nπ+5π6)sin⁡(2nπ−5π6),where\sin \left(2 n \pi+\frac{5 \pi}{6}\right) \sin \left(2 n \pi-\frac{5 \pi}{6}\right), where n \in Z??

Options

  1. A14\frac{1}{4}
  2. B−34-\frac{3}{4}
  3. C−14-\frac{1}{4}
  4. D34\frac{3}{4}

Correct answer

A. 14\frac{1}{4}

Step-by-step solution

sin⁡(2nπ+5π6)sin⁡(2nπ−5π6)=−sin⁡5π6⋅sin⁡(5π6)=−sin⁡2(π−π6)=−sin⁡2π6=−14\begin{aligned} & \sin \left(2 n \pi+\frac{5 \pi}{6}\right) \sin \left(2 n \pi-\frac{5 \pi}{6}\right) \\ & =-\sin \frac{5 \pi}{6} \cdot \sin \left(\frac{5 \pi}{6}\right)=-\sin ^2\left(\pi-\frac{\pi}{6}\right) \\ & =-\sin ^2 \frac{\pi}{6}=-\frac{1}{4}\end{aligned}
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