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Question

The value of sinhx+2πni is


A

ex+e-x2

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B

ex-e-x2

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C

ex-e-x2i

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D

ex+e-x2i

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Solution

The correct option is B

ex-e-x2


The explanation for the correct option

The given trigonometric expression: sinhx+2πni.

sinhx+2πni=ex+2πni-e-x+2πni2sinhx+2πni=ex×e2πni-e-x×e-2πni2sinhx+2πni=excos2πn+isin2πn-e-xcos-2πn+isin-2πn2sinhx+2πni=ex1+i·0-e-x1+i·02sinhx+2πni=ex-e-x2

Therefore, the value of sinhx+2πni is ex-e-x2.

Hence, the correct option is (B).


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