vereinfachen ((cot(A)+csc(A))(cot(A)-csc(A)))/((1-cos(A))(1+cos(A)))

Lösung

vereinfachen

\frac{( cot ( A ) + csc ( A ) ) ( cot ( A ) - csc ( A ) )}{( 1 - cos ( A ) ) ( 1 + cos ( A ) )}

- csc^{2} (A)

Schritte zur Lösung

\frac{( cot ( A ) + csc ( A ) ) ( cot ( A ) - csc ( A ) )}{( 1 - cos ( A ) ) ( 1 + cos ( A ) )}

Vereinfache

(cot (A) + csc (A)) (cot (A) - csc (A)) : - 1

= \frac{- 1}{( 1 - cos ( A ) ) ( 1 + cos ( A ) )}

Wende Bruchregel an:

\frac{- a}{b} = - \frac{a}{b}

= - \frac{1}{( 1 - cos ( A ) ) ( 1 + cos ( A ) )}

(1 + cos (A)) (1 - cos (A)) = sin^{2} (A)

= - \frac{1}{sin ^{2} ( A )}

Vereinfache

\frac{1}{sin ^{2} ( A )} : csc^{2} (A)

= - csc^{2} (A)

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

e x p an d (5 - 3 \frac{x}{30517578125})^{20}

s im pl i f y sin (x) (cot (x) - csc (x)) + 1

e x p an d \frac{20}{( s ^{2} + 6 s + 25 ) ( s + 1 )}

e x p an d (5 + x^{3}) e^{2 x}