Limits, Continuity & Differentiability
Periodic Functions
Grade 12
Question:
<p>$\sin ax + \cos ax$ and $|\cos x| + |\sin x|$ are periodic functions of same fundamental period, if '$a$' equals</p>
<p>(a) 0</p>
<p>(b) 1</p>
<p>(c) 2</p>
<p>(d) 4</p>
Step-by-Step Solution
Key Concept: Equate the fundamental periods of two functions to find the unknown parameter value.
<p><strong>Solution:</strong></p><p>Fundamental period of $|\sin x| + |\cos x|$ is $\frac{\pi}{2}$.</p><p>Fundamental period of $(\sin ax + \cos ax)$ is $\frac{2\pi}{a}$.</p><p>For same fundamental period: $\frac{2\pi}{a} = \frac{\pi}{2}$</p><p>$a = 4$</p><p>Hence, (d) is the correct answer.</p>
Correct Answer: d