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NDA 2020
Exam
NDA
Year
2020
Subject
Mathematics
Chapter
Trigonometric Ratios & Identities

NDA 2020 · Mathematics · Trigonometric Ratios & Identities

What is the maximum value of x · x ?

What is the maximum value of sin⁡x⋅cos⁡x\sin x \cdot \cos x ?

Options

  1. A2
  2. B1
  3. C12\frac{1}{2}
  4. D222 \sqrt{2}

Correct answer

C. 12\frac{1}{2}

Step-by-step solution

y=sin⁡x⋅cos⁡x=2sin⁡x⋅cos⁡x2=sin⁡2x2y=\sin x \cdot \cos x=\frac{2 \sin x \cdot \cos x}{2}=\frac{\sin 2 x}{2} Now, maximum value of sin⁡2x=1\sin 2 x=1. ∴ymax⁡=12\therefore y_{\max }=\frac{1}{2}. \text{. }
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