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Previous Year Question (PYQs)
3
Period of the function $f(x) = \cos\left(\dfrac{2x}{3}\right) - \sin\left(\dfrac{4x}{5}\right)$ is:
Solution
Period of $\cos(\dfrac{2x}{3}) = \dfrac{2\pi}{(2/3)} = 3\pi$.
Period of $\sin(\dfrac{4x}{5}) = \dfrac{2\pi}{(4/5)} = \dfrac{5\pi}{2}.$
L.C.M. of $3\pi$ and $\dfrac{5\pi}{2}$ = $15\pi$.
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