erweitern (sin^6(x)+cos^6(x)-1)(sec^2(x)+csc^2(x))

Lösung

erweitern

(sin^{6} (x) + cos^{6} (x) - 1) (sec^{2} (x) + csc^{2} (x))

sin^{6} (x) sec^{2} (x) + sin^{6} (x) csc^{2} (x) + cos^{6} (x) sec^{2} (x) + cos^{6} (x) csc^{2} (x) - sec^{2} (x) - csc^{2} (x)

Schritte zur Lösung

(sin^{6} (x) + cos^{6} (x) - 1) (sec^{2} (x) + csc^{2} (x))

Setze Klammern

= sin^{6} (x) sec^{2} (x) + sin^{6} (x) csc^{2} (x) + cos^{6} (x) sec^{2} (x) + cos^{6} (x) csc^{2} (x) - 1 \cdot sec^{2} (x) - 1 \cdot csc^{2} (x)

Vereinfache

sin^{6} (x) sec^{2} (x) + sin^{6} (x) csc^{2} (x) + cos^{6} (x) sec^{2} (x) + cos^{6} (x) csc^{2} (x) - 1 \cdot sec^{2} (x) - 1 \cdot csc^{2} (x) : sin^{6} (x) sec^{2} (x) + sin^{6} (x) csc^{2} (x) + cos^{6} (x) sec^{2} (x) + cos^{6} (x) csc^{2} (x) - sec^{2} (x) - csc^{2} (x)

= sin^{6} (x) sec^{2} (x) + sin^{6} (x) csc^{2} (x) + cos^{6} (x) sec^{2} (x) + cos^{6} (x) csc^{2} (x) - sec^{2} (x) - csc^{2} (x)

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

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

e x p an d \frac{1}{( x + 4 ) ^{2}}

e x p an d (x + 1) d x

e x p an d (1 - \frac{1}{4} x^{2})^{2}