faktorisieren sec^4(x)-tan^4(x)

Lösung

faktorisieren

sec^{4} (x) - tan^{4} (x)

(sec^{2} (x) + tan^{2} (x)) (sec (x) + tan (x)) (sec (x) - tan (x))

Schritte zur Lösung

sec^{4} (x) - tan^{4} (x)

sec^{4} (x) = (sec^{2} (x))^{2}

tan^{4} (x) = (tan^{2} (x))^{2}

= (sec^{2} (x))^{2} - (tan^{2} (x))^{2}

Wende Formel zur Differenz von zwei Quadraten an:

x^{2} - y^{2} = (x + y) (x - y)

(sec^{2} (x))^{2} - (tan^{2} (x))^{2} = (sec^{2} (x) + tan^{2} (x)) (sec^{2} (x) - tan^{2} (x))

= (sec^{2} (x) + tan^{2} (x)) (sec^{2} (x) - tan^{2} (x))

Faktorisiere

sec^{2} (x) - tan^{2} (x) : (sec (x) + tan (x)) (sec (x) - tan (x))

= (sec^{2} (x) + tan^{2} (x)) (sec (x) + tan (x)) (sec (x) - tan (x))

s im pl i f y \frac{( 5 i ) ^{4}}{( 4 - 3 i ) ^{2}}

s im pl i f y 1 - 2 sin^{2} (x)

s im pl i f y \frac{sec ^{2} ( x ) - 1}{sec ^{2} ( x )}

s im pl i f y \frac{4}{5 + 1} + 1

s im pl i f y 9 + 220 - 21 + 280