erweitern sqrt((-2sin(t))^2+(2cos(t))^2+(4cos(t)-2sin(t))^2)

Lösung

erweitern

(- 2 sin (t))^{2} + (2 cos (t))^{2} + (4 cos (t) - 2 sin (t))^{2}

2 2 sin^{2} (t) + 5 cos^{2} (t) - 2 sin (2 t)

Schritte zur Lösung

(- 2 sin (t))^{2} + (2 cos (t))^{2} + (4 cos (t) - 2 sin (t))^{2}

(- 2 sin (t))^{2} = 2^{2} sin^{2} (t)

(2 cos (t))^{2} = 2^{2} cos^{2} (t)

= 2^{2} sin^{2} (t) + 2^{2} cos^{2} (t) + (4 cos (t) - 2 sin (t))^{2}

2^{2} = 4

= 4 sin^{2} (t) + 4 cos^{2} (t) + (4 cos (t) - 2 sin (t))^{2}

Multipliziere aus

4 sin^{2} (t) + 4 cos^{2} (t) + (4 cos (t) - 2 sin (t))^{2} : 8 sin^{2} (t) + 20 cos^{2} (t) - 16 cos (t) sin (t)

= 8 sin^{2} (t) + 20 cos^{2} (t) - 16 cos (t) sin (t)

Faktorisiere

8 sin^{2} (t) + 20 cos^{2} (t) - 16 cos (t) sin (t) : 4 (2 sin^{2} (t) + 5 cos^{2} (t) - 4 cos (t) sin (t))

= 4 (2 sin^{2} (t) + 5 cos^{2} (t) - 4 cos (t) sin (t))

Wende Radikal Regel an:

n ab = n a n b,

angenommen

a \geq 0, b \geq 0

= 4 2 sin^{2} (t) + 5 cos^{2} (t) - 4 cos (t) sin (t)

4 = 2

= 2 2 sin^{2} (t) + 5 cos^{2} (t) - 4 cos (t) sin (t)

2 sin^{2} (t) + 5 cos^{2} (t) - 4 cos (t) sin (t) = 2 sin^{2} (t) + 5 cos^{2} (t) - 2 sin (2 t)

= 2 2 sin^{2} (t) + 5 cos^{2} (t) - 2 sin (2 t)

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

e x p an d (9 + cos (θ))^{3}

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

e x p an d \frac{10 ( 29 e ^{30} + 1 )}{3 e ^{30}}

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