erweitern (sin^4(x)+cos^4(x-1))(sec^2(x)+csc^2(x))

Lösung

erweitern

(sin^{4} (x) + cos^{4} (x - 1)) (sec^{2} (x) + csc^{2} (x))

sin^{4} (x) sec^{2} (x) + sin^{4} (x) csc^{2} (x) + cos^{4} (x - 1) sec^{2} (x) + cos^{4} (x - 1) csc^{2} (x)

Schritte zur Lösung

(sin^{4} (x) + cos^{4} (x - 1)) (sec^{2} (x) + csc^{2} (x))

Wende Ausklammerungsregel an (VANI):

(a + b) (c + d) = a c + a d + b c + b d

(sin^{4} (x) + cos^{4} (x - 1)) (sec^{2} (x) + csc^{2} (x)) = sin^{4} (x) sec^{2} (x) + sin^{4} (x) csc^{2} (x) + cos^{4} (x - 1) sec^{2} (x) + cos^{4} (x - 1) csc^{2} (x)

= sin^{4} (x) sec^{2} (x) + sin^{4} (x) csc^{2} (x) + cos^{4} (x - 1) sec^{2} (x) + cos^{4} (x - 1) csc^{2} (x)

e x p an d \frac{0.714 ( x ^{2} + 1.39 x + 1274209.9 )}{x ( x + 1.59 ) ( x ^{2} + 1.06 x + 1274212.3 )}

e x p an d - \frac{36 ( - x ^{2} + 1 )}{( x ^{2} + 3 ) ^{3}}

e x p an d \frac{( 6 - x ) ^{4}}{81}

s im pl i f y (x^{3} + \frac{1}{x ^{3}}) (x^{3} - \frac{1}{x ^{3}})

e x p an d \frac{x + 4}{( x + 5 ) ( x - 1 )}