Question

tan(x+iy)=u+iv prove that u² +v² =cos h²y-cos²x÷cosh²y-sin²x​

Answer 1

Answer:

tan(2iβ)=itanh(2β)

Step-by-step explanation:

because If tan(α+iβ)=(x+iy) then prove that:

x2+y2+2xcot2α=1

x2+y2−2ycoth2β=1

I think that using the concept of logarithm will helpful to solve the problem but I am not able to do so. A detail solution explaining the concept will be helpful.

Thanks in advance !

NB: After going through all the suggestion questions I think all my doubts are cleared with this : tan(x+yi)=α+βi⇒tan(x−yi)=α−βi?