Anong tunay na function ay (e ^ (ix) -e ^ (- ix)) / (ibig sabihin ^ (ix) + ibig sabihin ^ (- ix)) katumbas ng?

Sagot:

#tan (x) #

Paliwanag:

# e ^ (ix) = cos (x) + i sin (x) #

#cos (-x) = cos (x) #

#sin (-x) = -sin (x) #

Kaya:

# e ^ (ix) -e ^ (- ix) = (cos (x) + i sin (x)) - (cos (-x) + i sin (-x)) #

# = (cos (x) + i sin (x)) - (cos (x) -i sin (x)) = 2i kasalanan (x) #

At:

# e ^ (ix) + e ^ (- ix) = (cos (x) + i sin (x)) + (cos (-x) + i sin (-x)) #

# = (cos (x) + i sin (x)) + (cos (x) -i sin (x)) = 2 cos (x) #

Kaya:

(x)) / (2i cos (x)) = kasalanan (x)) / cos (x) = tan (x) #