erweitern (xcos(θ)-ysin(θ))^2

Lösung

erweitern

(x cos (θ) - y sin (θ))^{2}

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

Schritte zur Lösung

(x cos (θ) - y sin (θ))^{2}

Wende Formel für perfekte quadratische Gleichungen an:

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

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

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

Vereinfache

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

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

\frac{\partial}{\partial x} ((z) (x^{2} y + 4 x + 3 y))

e x p an d \frac{( x + 4 ) ( x - 3 ) ^{2}}{x ^{4} ( x - 1 )}

e x p an d (x + 5)^{4}

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

e x p an d (cos (β) - 1) (sin (β) - 1)