Ken T.

asked • 01/15/18

Functions of Complex variables

Sin(Θ+iΦ)=cosα+i*sinα
prove that 
cos^4(Θ)=sin^2(α)=sinh^4(Φ)

1 Expert Answer

By:

Bobosharif S. answered • 01/15/18

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Mathematics/Statistics Tutor

Ken T.

Could you please explain
 
Sin^2(α) part
Report

01/16/18

Ken T.

How is Sin^2(α) =sinh^4(Φ)=cos^4(Θ)
Report

01/16/18

Bobosharif S.

Hello again,
 
sin(Θ)cosh(Φ)+i cos(Θ)sinh(Φ)=cosα+i*sinα
 
So,
sinα=cos(Θ)sinh(Φ) (1)
cosα=sin(Θ)cosh(Φ) (2)
 
As before,
sin2α=cos2(Θ)sinh2(Φ)=|from (2) find sinh2(Φ) and plug in here|=
=...=cot2(Θ)*cot2(Θ)*sin2α-cos2(Θ).
 
and 
sin2α=cos4(Θ).
The other part is similar... I hope you get it done easily. If not let me know.
 
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01/16/18

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