Jamia Millia Islamia MCA Trigonometrical Function Previous Year Questions (PYQs)
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Period of $3\sec x/3$ is
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Solution
Period of $\sec kx$ = $\dfrac{2\pi}{k}$ → here $k = 1/3$.
Hence period = $6\pi$.
What will be the value of
$f(x) = (\sin 3x + \sin x)\sin x + (\cos 3x - \cos x)\cos x$ ?
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Solution
$f(x) = (\sin 3x + \sin x)\sin x + (\cos 3x - \cos x)\cos x$
$= \sin 3x \sin x + \sin^2 x + \cos 3x \cos x - \cos^2 x$
Using identity $\cos A \cos B + \sin A \sin B = \cos(A - B)$:
$f(x) = \cos(3x - x) + (\sin^2 x - \cos^2 x)$
$= \cos 2x - \cos 2x = 0$
Period of the function $f(x) = \cos\left(\dfrac{2x}{3}\right) - \sin\left(\dfrac{4x}{5}\right)$ is:
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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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