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NDA 2021
Exam
NDA
Year
2021
Subject
Mathematics
Chapter
Trigonometric Ratios & Identities

NDA 2021 · Mathematics · Trigonometric Ratios & Identities

Let x+ y= x+ y for all x, y ∈ ℝ . What is ((x)/(2)+(y)/(2))equal to?

Let sin⁡x+sin⁡y=cos⁡x+cos⁡y\sin x+\sin y=\cos x+\cos y for all x,y∈Rx, y \in \mathbb{R}. What is tan⁡(x2+y2)equalto?\tan \left(\frac{x}{2}+\frac{y}{2}\right)equal to?

Options

  1. A1
  2. B2
  3. C2\sqrt{2}
  4. D222 \sqrt{2}

Correct answer

A. 1

Step-by-step solution

Given. sin⁡x+sin⁡y=cos⁡x+cos⁡y2sin⁡(x+y2)cos⁡(x−y2)=2cos⁡(x+y2)cos⁡(x−y2)\begin{aligned} & \sin x+\sin y=\cos x+\cos y \\ & 2 \sin \left(\frac{x+y}{2}\right) \cos \left(\frac{x-y}{2}\right) \\ & =2 \cos \left(\frac{x+y}{2}\right) \cos \left(\frac{x-y}{2}\right) \end{aligned} On dividing $2 \cos \left(\frac{x+y}{2}\right) \cdot \cos\left(\frac{x-y}{2}\right) both side \tan \left(\frac{x+y}{2}\right)=1
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