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Question

The period of 3sin(2x+π3)4cos(πxπ6) is

A
1
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B
π
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C
2+π
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D
Not defined
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Solution

The correct option is D Not defined
We know that, period of both a+bsin(mx+n) and a+bcos(mx+n) is 2π|m|.
Hence, period of 3sin(2x+π3) is π and period of 4cos(πxπ6) is 2.

Therefore, period of 3sin(2x+π3)4cos(πxπ6)
=LCM of (π,2)
2 is a rational number and π is an irrational number.As the L.C.M of a rational and irrational is not defined.

Hence, period of 3sin(2x+π3)4cos(πxπ6) is undefined.

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