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Question

Evaluate: sechπi+cosechπ2i


A

1-i

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B

-1+i

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C

-1-i

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D

1+i

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Solution

The correct option is C

-1-i


Explanation for the correct option:

Using the complex hyperbolic function definition:

Put the values of the hyperbolic function definition in the given relation.

sechπi+cosechπ2i=secπ-icosecπ2 sech(xi)=sec(x)&cosech(xi)=-icosec(x)

Put the values of the trigonometric functions to get the solution.

sechπi+cosechπ2i=-1-isechπ=-1andcosechπ2=1

Hence, option (C) is the correct answer.


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