erweitern (cos(x)+ysin(x))^2

Lösung

erweitern

(cos (x) + y sin (x))^{2}

cos^{2} (x) + y^{2} sin^{2} (x) + y sin (2 x)

Schritte zur Lösung

(cos (x) + y sin (x))^{2}

Wende Formel für perfekte quadratische Gleichungen an:

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

(cos (x) + y sin (x))^{2} = cos^{2} (x) + 2 cos (x) y sin (x) + (y sin (x))^{2}

= cos^{2} (x) + 2 cos (x) y sin (x) + (y sin (x))^{2}

Vereinfache

cos^{2} (x) + 2 cos (x) y sin (x) + (y sin (x))^{2} : cos^{2} (x) + y^{2} sin^{2} (x) + y sin (2 x)

= cos^{2} (x) + y^{2} sin^{2} (x) + y sin (2 x)

e x p an d P (2, - 3) A (c + 2, - 4) B (4 - 3 c, - 2)

e x p an d l im x \Rightarrow 2 (3 x^{3} - 2 x^{2} + 6 x)

s im pl i f y (5 - x + 2)^{2}

e x p an d 3 (13 + 7)

e x p an d - (\frac{s ^{3} + s ^{2} + 6 s - 2}{s ( s + 3 ) ( s - 1 )})