erweitern (1+tan^4(t/(12)))^3

Lösung

erweitern

(1 + tan^{4} (\frac{t}{12}))^{3}

1 + 3 tan^{4} (\frac{t}{12}) + 3 tan^{8} (\frac{t}{12}) + tan^{12} (\frac{t}{12})

Schritte zur Lösung

(1 + tan^{4} (\frac{t}{12}))^{3}

Wende Formel für perfekte dritte Potenzen an:

(a + b)^{3} = a^{3} + 3 a^{2} b + 3 a b^{2} + b^{3}

(1 + tan^{4} (\frac{t}{12}))^{3} = 1^{3} + 3 \cdot 1^{2} tan^{4} (\frac{t}{12}) + 3 \cdot 1 \cdot (tan^{4} (\frac{t}{12}))^{2} + (tan^{4} (\frac{t}{12}))^{3}

= 1^{3} + 3 \cdot 1^{2} tan^{4} (\frac{t}{12}) + 3 \cdot 1 \cdot (tan^{4} (\frac{t}{12}))^{2} + (tan^{4} (\frac{t}{12}))^{3}

1^{3} = 1

3 \cdot 1^{2} tan^{4} (\frac{t}{12}) = 3 tan^{4} (\frac{t}{12})

3 \cdot 1 \cdot (tan^{4} (\frac{t}{12}))^{2} = 3 tan^{8} (\frac{t}{12})

(tan^{4} (\frac{t}{12}))^{3} = tan^{12} (\frac{t}{12})

= 1 + 3 tan^{4} (\frac{t}{12}) + 3 tan^{8} (\frac{t}{12}) + tan^{12} (\frac{t}{12})

s im pl i f y (t - \frac{1}{2}) (t^{2} - t + \frac{1}{6})

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

e x p an d - cos (v) sin (u) (2 cos (v) + cos (v) cos (u))

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

e x p an d (sin (2 t) + 2 sin (t)) \cdot (2 sin (t) - 2 sin (2 t))