erweitern (1+cos^2(x))^2

Lösung

erweitern

(1 + cos^{2} (x))^{2}

1 + 2 cos^{2} (x) + cos^{4} (x)

Schritte zur Lösung

(1 + cos^{2} (x))^{2}

Wende Formel für perfekte quadratische Gleichungen an:

(a + b)^{2} = a^{2} + 2 ab + b^{2}

(1 + cos^{2} (x))^{2} = 1^{2} + 2 \cdot 1 \cdot cos^{2} (x) + (cos^{2} (x))^{2}

= 1^{2} + 2 \cdot 1 \cdot cos^{2} (x) + (cos^{2} (x))^{2}

Vereinfache

1^{2} + 2 \cdot 1 \cdot cos^{2} (x) + (cos^{2} (x))^{2} : 1 + 2 cos^{2} (x) + cos^{4} (x)

= 1 + 2 cos^{2} (x) + cos^{4} (x)

e x p an d \frac{x ^{2} + 9 x - 42}{( x + 1 ) ( x + 6 )}

e x p an d (2 x - 1) d x + (3 y + 7) d y

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

s im pl i f y (\frac{1}{2} + \frac{1}{2} cos (2 x))^{4}

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