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NDA 2019
Exam
NDA
Year
2019
Subject
Mathematics
Chapter
Trigonometric Ratios & Identities

NDA 2019 · Mathematics · Trigonometric Ratios & Identities

Paragraph: Consider the function f(x)=g(x)+h(x) where g(x)=...

Paragraph: Consider the function f(x)=g(x)+h(x)f(x)=g(x)+h(x) where g(x)=sin⁡(x4)g(x)=\sin \left(\frac{x}{4}\right)and h(x)=\cos \left(\frac{4 x}{5}\right)<br><strong>Question:</strong>Whatistheperiodofthefunction<br><strong>Question:</strong> What is the period of the functionf(x) ?

Options

  1. A10π10 \pi
  2. B20π20 \pi
  3. C40π40 \pi
  4. D80π80 \pi

Correct answer

C. 40π40 \pi

Step-by-step solution

Period of f(x)=f(x)= LCM of period of g(x)&h(x)g(x) \& h(x)⇒LCM[8π,5π2]=40π\begin{aligned} & \Rightarrow \quad \mathrm{LCM}\left[8 \pi, \frac{5 \pi}{2}\right] \\ & =40 \pi \end{aligned}$$
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