vereinfachen (e^{iθ}+e^{-iθ})^3

Lösung

vereinfachen

(e^{i θ} + e^{- i θ})^{3}

8 cos^{3} (θ)

Schritte zur Lösung

(e^{i θ} + e^{- i θ})^{3}

e^{i θ} = cos (θ) + i sin (θ)

e^{- i θ} = cos (θ) - i sin (θ)

= (cos (θ) + i sin (θ) + cos (θ) - i sin (θ))^{3}

Vereinfache

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

= (2 cos (θ))^{3}

Wende Exponentenregel an:

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

= 2^{3} cos^{3} (θ)

2^{3} = 8

= 8 cos^{3} (θ)

e x p an d \frac{3 - 6 e ^{- 2 s}}{( s + 2 ) ( s + 3 )}

e x p an d (2 x y + 3 yz) d x - (2 x y + x^{2}) d y

e x p an d \frac{( 1 - x ) ^{2}}{3}

e x p an d \frac{5}{( s ^{2} + 25 ) ( s + 1 ) ( s + 2 )}

\frac{d}{d t} ((x) (x + 3 y))