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Question

Question: \({\sin h}\left( x + \frac{\pi i}{2} \right)\) equals....

sin⁡h(x+πi2){\sin h}\left( x + \frac{\pi i}{2} \right) equals.

A

icosh⁡xi\cosh x

B

−icosh⁡x- i\cosh x

C

cos⁡x\cos x

D

−cos⁡x- \cos x

Answer

icosh⁡xi\cosh x

Explanation

Solution

sinh⁡(x+π2i)=−isin⁡(ix−π2)=isin⁡(π2−ix)\sinh\left( x + \frac{\pi}{2}i \right) = - i\sin\left( ix - \frac{\pi}{2} \right) = i\sin\left( \frac{\pi}{2} - ix \right)

=icos⁡(ix)=icos⁡hx= i\cos(ix) = i{\cos h}x.