erweitern (e^{ix}+e^{-ix})^2

Lösung

erweitern

(e^{i x} + e^{- i x})^{2}

4 cos^{2} (x)

Schritte zur Lösung

(e^{i x} + e^{- i x})^{2}

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

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

= (cos (x) + i sin (x) + cos (x) - i sin (x))^{2}

Vereinfache

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

= (2 cos (x))^{2}

Wende Exponentenregel an:

(a \cdot b)^{n} = a^{n} b^{n}

= 2^{2} cos^{2} (x)

2^{2} = 4

= 4 cos^{2} (x)

e x p an d A (3, 0, - 1) B (0, - 2, 0)

e x p an d \frac{3.0685}{x ( x + 0.2933 )}

e x p an d (a + c = 40, 0) (25 a + 15 c = 7550)

e x p an d \frac{2 n}{n + 4} + \frac{7}{n - 1}

e x p an d \frac{( e ^{\frac{x}{a}} - e ^{- \frac{x}{a}} ) ^{2}}{4}