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

NDA 2023 · Mathematics · Trigonometric Ratios & Identities

Paragraph: Let f(x)= [π^2] x+ [-π^2] x where [.] is a greatest...

Paragraph: Let f(x)=sin⁡[π2]x+cos⁡[−π2]xf(x)=\sin \left[\pi^2\right] x+\cos \left[-\pi^2\right] x where [.] is a greatest integer function.
Question: What is f(π4)equalto?f \left(\frac{\pi}{4}\right)equal to?

Options

  1. A−12-\frac{1}{\sqrt{2}}
  2. B−1-1
  3. C11
  4. D12\frac{1}{\sqrt{2}}

Correct answer

D. 12\frac{1}{\sqrt{2}}

Step-by-step solution

f(π4)=sin⁡9π4+cos⁡10π4=sin⁡(2π+π4)+cos⁡(2π+π2)=sin⁡π4+cos⁡π2=12f\left(\frac{\pi}{4}\right)=\sin \frac{9 \pi}{4}+\cos \frac{10 \pi}{4}=\sin \left(2 \pi+\frac{\pi}{4}\right)+\cos \left(2 \pi+\frac{\pi}{2}\right)=\sin \frac{\pi}{4}+\cos \frac{\pi}{2}=\frac{1}{\sqrt{2}}
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