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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 sin⁡3x+sin⁡3y?\sin 3 x+\sin 3 y ?

Options

  1. A-1
  2. B0
  3. C1
  4. D3

Correct answer

B. 0

Step-by-step solution

 Since, sin⁡3x+sin⁡3y=sin⁡(3⋅5π12)+sin⁡(3⋅π12)=−sin⁡(π/4)+sin⁡(π/4)=0\begin{aligned} & \text{ Since, } \sin 3 \mathrm{x}+\sin 3 \mathrm{y} \\ & =\sin \left(3 \cdot \frac{5 \pi}{12}\right)+\sin \left(3 \cdot \frac{\pi}{12}\right) \\ & =-\sin (\pi / 4)+\sin (\pi / 4)=0\end{aligned}
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