erweitern (-3sin(x)+3sin(3x))^2+(3cos(x)-cos(3x)*3)^2

Lösung

erweitern

(- 3 sin (x) + 3 sin (3 x))^{2} + (3 cos (x) - cos (3 x) \cdot 3)^{2}

36 sin^{2} (x)

Schritte zur Lösung

(- 3 sin (x) + 3 sin (3 x))^{2} + (3 cos (x) - cos (3 x) \cdot 3)^{2}

Schreibe

(- 3 sin (x) + 3 sin (3 x))^{2}

um:

9 sin^{2} (x) - 18 sin (x) sin (3 x) + 9 sin^{2} (3 x)

= 9 sin^{2} (x) - 18 sin (x) sin (3 x) + 9 sin^{2} (3 x) + (3 cos (x) - cos (3 x) \cdot 3)^{2}

Schreibe

(3 cos (x) - cos (3 x) \cdot 3)^{2}

um:

9 cos^{2} (x) - 18 cos (x) cos (3 x) + 9 cos^{2} (3 x)

= 9 sin^{2} (x) - 18 sin (x) sin (3 x) + 9 sin^{2} (3 x) + 9 cos^{2} (x) - 18 cos (x) cos (3 x) + 9 cos^{2} (3 x)

Vereinfache

9 sin^{2} (x) - 18 sin (x) sin (3 x) + 9 sin^{2} (3 x) + 9 cos^{2} (x) - 18 cos (x) cos (3 x) + 9 cos^{2} (3 x) : 36 sin^{2} (x)

= 36 sin^{2} (x)

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

e x p an d (e^{x} - 2) e^{x}

s im pl i f y 6 (7 d + \frac{1}{2})

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

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