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Beliebt Algebra >

erweitern (f'(t)sin(t)+f(t)cos(t))^2

Lösung

erweitern

(f^{'} (t) sin (t) + f (t) cos (t))^{2}

Lösung

sin^{2} (t) (f' (t))^{2} + 2 sin (t) cos (t) f' (t) f (t) + cos^{2} (t) f (t)^{2}

Schritte zur Lösung

(f^{'} (t) sin (t) + f (t) cos (t))^{2}

= (sin (t) f^{^{'}} (t) + cos (t) f (t))^{2}

Wende Formel für perfekte quadratische Gleichungen an:

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

a = f^{'} (t) sin (t), b = f (t) cos (t)

= (f^{^{'}} (t) sin (t))^{2} + 2 f^{^{'}} (t) sin (t) f (t) cos (t) + (f (t) cos (t))^{2}

Vereinfache

(f^{'} (t) sin (t))^{2} + 2 f^{'} (t) sin (t) f (t) cos (t) + (f (t) cos (t))^{2} : sin^{2} (t) (f^{'} (t))^{2} + 2 sin (t) cos (t) f^{'} (t) f (t) + cos^{2} (t) f (t)^{2}

= sin^{2} (t) (f^{'} (t))^{2} + 2 sin (t) cos (t) f^{'} (t) f (t) + cos^{2} (t) f (t)^{2}

Beliebte Beispiele

erweitern (sin(x/2)+cos(x/2))^2-sin(x)

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

vereinfachen (x+3-2sqrt(3))(x+3+2sqrt(3))

s im pl i f y (x + 3 - 23) (x + 3 + 23)

vereinfachen (z-1/2)(z-1/5)

s im pl i f y (z - \frac{1}{2}) (z - \frac{1}{5})

erweitern (2x^2-3)/((x-1)^2)

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

erweitern (25)/((t+1)^2)

e x p an d \frac{25}{( t + 1 ) ^{2}}