erweitern (1-cos(x))^2csc^2(x)

Lösung

erweitern

(1 - cos (x))^{2} csc^{2} (x)

csc^{2} (x) - 2 csc^{2} (x) cos (x) + csc^{2} (x) cos^{2} (x)

Schritte zur Lösung

(1 - cos (x))^{2} csc^{2} (x)

= csc^{2} (x) (1 - cos (x))^{2}

Schreibe

(1 - cos (x))^{2}

um:

1 - 2 cos (x) + cos^{2} (x)

= csc^{2} (x) (1 - 2 cos (x) + cos^{2} (x))

Wende das Distributivgesetz an:

m (a + b + c) = ma + mb + m c

csc^{2} (x) (1 - 2 cos (x) + cos^{2} (x)) = csc^{2} (x) \cdot 1 + csc^{2} (x) (- 2 cos (x)) + csc^{2} (x) cos^{2} (x)

= csc^{2} (x) \cdot 1 + csc^{2} (x) (- 2 cos (x)) + csc^{2} (x) cos^{2} (x)

Vereinfache

csc^{2} (x) \cdot 1 + csc^{2} (x) (- 2 cos (x)) + csc^{2} (x) cos^{2} (x) : csc^{2} (x) - 2 csc^{2} (x) cos (x) + csc^{2} (x) cos^{2} (x)

= csc^{2} (x) - 2 csc^{2} (x) cos (x) + csc^{2} (x) cos^{2} (x)

e x p an d (4, - 6 i) (4 + 6 i)

e x p an d y^{\frac{1}{4}} (y^{\frac{3}{4}} + y^{\frac{7}{4}})

e x p an d \frac{2 \cdot ( x + y ) ^{2}}{3}

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

e x p an d (a sin (t) cos (p) - d sin (p))^{2}