A) \[y=\sin \left( 2\pi t+\frac{\pi }{3} \right)+2\sin \left( 3\pi t+\frac{\pi }{4} \right)+3\sin 5\pi t\]
B) \[y=\sin \frac{\pi }{3}t+\sin \frac{\pi }{4}t\]
C) \[y\sin t+\cos 2t\]
D) None of these
Correct Answer: C
Solution :
We have two functions \[f(x)\]and \[g(x)\] have periods \[{{T}_{1}}\] and \[{{T}_{2}}\] respectively, then each of \[f(x)\pm g(x);\] \[f(x).g(x);\]\[f(x)/g(x),\] provided \[g(x)=0\]has period equal to the LCM of \[{{T}_{1}}\] and \[{{T}_{2}}\]. Now, we know that \[sin\text{ }x\]or \[cos\text{ }x\]has period \[2\pi \] Hence period of \[y=\sin t+\cos 2t\]is \[2\pi \].
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