vereinfachen (e^{iwt}+e^{-iwt})e^{-iwt}

Lösung

vereinfachen

(e^{i wt} + e^{- i wt}) e^{- i wt}

2 cos^{2} (wt) - 2 i cos (wt) sin (wt)

Schritte zur Lösung

(e^{i wt} + e^{- i wt}) e^{- i wt}

e^{i wt} = cos (wt) + i sin (wt)

e^{- i wt} = cos (wt) - i sin (wt)

= e^{- i wt} (cos (wt) + cos (wt) + i sin (wt) - i sin (wt))

e^{- i wt} = cos (wt) - i sin (wt)

= (cos (wt) + cos (wt) + i sin (wt) - i sin (wt)) (cos (wt) - i sin (wt))

Vereinfache

cos (wt) + sin (wt) i + cos (wt) - i sin (wt) : 2 cos (wt)

= 2 cos (wt) (cos (wt) - i sin (wt))

Schreibe

2 cos (wt) (cos (wt) - i sin (wt))

in der Standard komplexen Form um:

2 cos^{2} (wt) - 2 cos (wt) sin (wt) i

= 2 cos^{2} (wt) - 2 cos (wt) sin (wt) i

e x p an d \frac{7 ( a + h ) - 6}{( a + h ) - 8}

e x p an d \frac{5 ( x + 2 )}{2 x - 14}

e x p an d y (2 x + 3 y = - 2)

e x p an d \frac{( 3 x + 1 ) ( 3 x - 1 )}{9}

e x p an d 2.12 + 6