faktorisieren sin^{2007}(x)+cos^{2007}(x)

Lösung

faktorisieren

sin^{2007} (x) + cos^{2007} (x)

(sin^{223} (x) + cos^{223} (x)) (sin^{446} (x) - sin^{223} (x) cos^{223} (x) + cos^{446} (x)) (sin^{1338} (x) - sin^{669} (x) cos^{669} (x) + cos^{1338} (x))

Schritte zur Lösung

sin^{2007} (x) + cos^{2007} (x)

Schreibe

sin^{2007} (x) + cos^{2007} (x)

um:

(sin^{669} (x))^{3} + (cos^{669} (x))^{3}

= (sin^{669} (x))^{3} + (cos^{669} (x))^{3}

Wende Formel zur Summe von dritten Potenzen an:

x^{3} + y^{3} = (x + y) (x^{2} - x y + y^{2})

(sin^{669} (x))^{3} + (cos^{669} (x))^{3} = (sin^{669} (x) + cos^{669} (x)) (sin^{1338} (x) - sin^{669} (x) cos^{669} (x) + cos^{1338} (x))

= (sin^{669} (x) + cos^{669} (x)) (sin^{1338} (x) - sin^{669} (x) cos^{669} (x) + cos^{1338} (x))

Faktorisiere

sin^{669} (x) + cos^{669} (x) : (sin^{223} (x) + cos^{223} (x)) (sin^{446} (x) - sin^{223} (x) cos^{223} (x) + cos^{446} (x))

= (sin^{223} (x) + cos^{223} (x)) (sin^{446} (x) - sin^{223} (x) cos^{223} (x) + cos^{446} (x)) (sin^{1338} (x) - sin^{669} (x) cos^{669} (x) + cos^{1338} (x))

f a c t or \frac{x}{x ^{2}}

f a c t or f^{13} (21)

f a c t or (- x) - 1

f a c t or \frac{x ^{2} + 3 x}{x}

f a c t or [(2 t + 1) + t^{2}]^{3}