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Question

Question: \(\cos ix + i\sin ix\) equals...

cos⁡ix+isin⁡ix\cos ix + i\sin ix equals

A

eixe^{ix}

B

e−ixe^{- ix}

C

exe^{x}

D

e−xe^{- x}

Answer

e−xe^{- x}

Explanation

Solution

cos⁡ix+isin⁡ix\cos ix + i\sin ix

= cosh⁡x+i.isinh⁡x\cosh x + i.i\sinh x = cos⁡hx−sin⁡hx=ex+e−x−ex+e−x2{\cos h}x - {\sin h}x = \frac{e^{x} + e^{- x} - e^{x} + e^{- x}}{2}

= e−xe^{- x}