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Question

If sin-1(A+iB)=x+iy, then AB=


A

tanxtanhy

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B

tanhxtany

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C

tanhxtanhy

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D

cosxcoshy

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Solution

The correct option is A

tanxtanhy


Explanation for the correct option.

Compute the required value:

Given that, sin-1(A+iB)=x+iy.

Taking sin both sides we have:

(A+iB)=sin(x+iy)(A+iB)=sinxcoshy+icosxsinhy

Comparing real & imaginary parts we have:

A=sinxcoshyB=cosxsinhy

Therefore the value is:

AB=[sinxcoshy][cosxsinhy]=tanxtanhy

Hence, option A is correct.


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