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Question

cosix+isinix=?


A

eix

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B

e-ix

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C

ex

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D

e-x

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Solution

The correct option is D

e-x


Explanation for the correct option:

Given, cosix+isinix

=coshx+i×isinhx ; cosix=coshx,sinix=isinhx

=coshxsinhx ; i2=1

=ex+e-x2ex-e-x2 ; cosh(x)=ex+e-x2,sinh(x)=ex-e-x2

=[ex+e-xex+e-x]2

=2e-x2

=e-x

Hence, Option ‘D’ is Correct.


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