cos (α +iβ ) is equal to

Question

cos (α +iβ ) is equal to (A)  cos text α text coch text β -2 text sin text α text sinh text β  (B)  cos text α text cosh text β +2 text sin text α text sinh text β  (C)  cosh text α text cos text β -2 text sinh text α text sin text β  (D) None of the above

Tardigrade Admin · Accepted Answer

cos (α +iβ )= cos α cos iβ - sin α sin iβ = cos α cosh β -i sin α sinh β

Q. $cos (α + i β)$ is equal to

$cos α coc h β - 2 s in α s inh β$

$cos α cos h β + 2 s in α s inh β$

$cos h α cos β - 2 s inh α s in β$

None of the above

$cos (α + i β) = cos α cos i β - sin α sin i β$ $= cos α cosh β - i sin α sinh β$

Q. cos(α+iβ) is equal to

cosαcochβ−2sinαsinhβ

cosαcoshβ+2sinαsinhβ

coshαcosβ−2sinhαsinβ