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Question

The value of sechiπ is


A

-1

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B

i

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C

0

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D

1

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Solution

The correct option is A

-1


Explanation for the correct answer:

Compute the required value:

we know that,

coshx=ex+e-x2

sechx=2ex+e-x

Substitute the value of x=iπ we get,

sechiπ=2eiπ+e-iπ

sechiπ=2cosπ+isinπ+cosπ-isinπ ...[eiθ=cosθ+isinθ]

sechiπ=22cosπ

sechiπ=secπ=-1

Hence, the value of sechiπ is -1.

Hence, option A is the correct answer.


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