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NDA 2023
Exam
NDA
Year
2023
Subject
Mathematics
Chapter
Trigonometric Ratios & Identities

NDA 2023 · Mathematics · Trigonometric Ratios & Identities

Let x+ y= 3 ( y- x) ; x+y=(π)/(2) , 0 < x, y < (π)/(2) What is a...

Let sin⁡x+sin⁡y=3(cos⁡y−cos⁡x);x+y=π2\sin x+\sin y=\sqrt{3}(\cos y-\cos x) ; x+y=\frac{\pi}{2}, 0<x,y<π20 < x, y < \frac{\pi}{2} What is a value of cos⁡3x+cos⁡3y\cos ^3 x+\cos ^3 y ?

Options

  1. A338\frac{3 \sqrt{3}}{8}
  2. B368\frac{3 \sqrt{6}}{8}
  3. C364\frac{3 \sqrt{6}}{4}
  4. D1

Correct answer

B. 368\frac{3 \sqrt{6}}{8}

Step-by-step solution

Since, cos⁡3(5π12)+cos⁡3(π12)=(3−122)3+(3+122)3=368\begin{aligned} & \cos ^3\left(\frac{5 \pi}{12}\right)+\cos ^3\left(\frac{\pi}{12}\right) \\ & =\left(\frac{\sqrt{3}-1}{2 \sqrt{2}}\right)^3+\left(\frac{\sqrt{3}+1}{2 \sqrt{2}}\right)^3=\frac{3 \sqrt{6}}{8} \end{aligned}
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