erweitern (xcos(a)+ycos(a+b)+zcos(a+b+c))^2

Lösung

erweitern

(x cos (a) + y cos (a + b) + z cos (a + b + c))^{2}

x^{2} cos^{2} (a) + x y cos (a) cos (a + b) + x z cos (a) cos (a + b + c) + x y cos (a + b) cos (a) + y^{2} cos^{2} (a + b) + yz cos (a + b) cos (a + b + c) + x z cos (a + b + c) cos (a) + yz cos (a + b + c) cos (a + b) + z^{2} cos^{2} (a + b + c)

Schritte zur Lösung

(x cos (a) + y cos (a + b) + z cos (a + b + c))^{2}

Wende Exponentenregel an:

a^{b + c} = a^{b} \cdot a^{c}

(x cos (a) + y cos (a + b) + z cos (a + b + c))^{2} = (x cos (a) + y cos (a + b) + z cos (a + b + c)) (x cos (a) + y cos (a + b) + z cos (a + b + c))

= (x cos (a) + y cos (a + b) + z cos (a + b + c)) (x cos (a) + y cos (a + b) + z cos (a + b + c))

Setze Klammern

= x cos (a) x cos (a) + x cos (a) y cos (a + b) + x cos (a) z cos (a + b + c) + y cos (a + b) x cos (a) + y cos (a + b) y cos (a + b) + y cos (a + b) z cos (a + b + c) + z cos (a + b + c) x cos (a) + z cos (a + b + c) y cos (a + b) + z cos (a + b + c) z cos (a + b + c)

Vereinfache

x cos (a) x cos (a) + x cos (a) y cos (a + b) + x cos (a) z cos (a + b + c) + y cos (a + b) x cos (a) + y cos (a + b) y cos (a + b) + y cos (a + b) z cos (a + b + c) + z cos (a + b + c) x cos (a) + z cos (a + b + c) y cos (a + b) + z cos (a + b + c) z cos (a + b + c) : x^{2} cos^{2} (a) + x y cos (a) cos (a + b) + x z cos (a) cos (a + b + c) + x y cos (a + b) cos (a) + y^{2} cos^{2} (a + b) + yz cos (a + b) cos (a + b + c) + x z cos (a + b + c) cos (a) + yz cos (a + b + c) cos (a + b) + z^{2} cos^{2} (a + b + c)

= x^{2} cos^{2} (a) + x y cos (a) cos (a + b) + x z cos (a) cos (a + b + c) + x y cos (a + b) cos (a) + y^{2} cos^{2} (a + b) + yz cos (a + b) cos (a + b + c) + x z cos (a + b + c) cos (a) + yz cos (a + b + c) cos (a + b) + z^{2} cos^{2} (a + b + c)

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

e x p an d cos (t) h (t - \frac{π}{2})

s im pl i f y \frac{3 ( 2 + 7 )}{3}

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

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