erweitern ((2(1-cot(2x))(sec^2(2x))-2(csc^2(2x))(tan(2x))))/((1-cot(2x))^2)

Lösung

erweitern

\frac{( 2 ( 1 - cot ( 2 x ) ) ( sec ^{2} ( 2 x ) ) - 2 ( csc ^{2} ( 2 x ) ) ( tan ( 2 x ) ) )}{( 1 - cot ( 2 x ) ) ^{2}}

\frac{2 sec ^{2} ( 2 x ) - 2 sec ^{2} ( 2 x ) cot ( 2 x ) - 2 csc ^{2} ( 2 x ) tan ( 2 x )}{- 2 cot ( 2 x ) + csc ^{2} ( 2 x )}

Schritte zur Lösung

\frac{2 ( 1 - cot ( 2 x ) ) ( sec ^{2} ( 2 x ) ) - 2 ( csc ^{2} ( 2 x ) ) ( tan ( 2 x ) )}{( 1 - cot ( 2 x ) ) ^{2}}

Entferne die Klammern:

(a) = a

= \frac{2 ( 1 - cot ( 2 x ) ) sec ^{2} ( 2 x ) - 2 csc ^{2} ( 2 x ) tan ( 2 x )}{( 1 - cot ( 2 x ) ) ^{2}}

(1 - cot (2 x))^{2} = 1 - 2 cot (2 x) + cot^{2} (2 x)

= \frac{2 sec ^{2} ( 2 x ) ( - cot ( 2 x ) + 1 ) - 2 csc ^{2} ( 2 x ) tan ( 2 x )}{1 - 2 cot ( 2 x ) + cot ^{2} ( 2 x )}

Vereinfache

1 - 2 cot (2 x) + cot^{2} (2 x) : csc^{2} (2 x) - 2 cot (2 x)

= \frac{2 sec ^{2} ( 2 x ) ( - cot ( 2 x ) + 1 ) - 2 csc ^{2} ( 2 x ) tan ( 2 x )}{- 2 cot ( 2 x ) + csc ^{2} ( 2 x )}

Multipliziere aus

2 (1 - cot (2 x)) sec^{2} (2 x) - 2 csc^{2} (2 x) tan (2 x) : 2 sec^{2} (2 x) - 2 sec^{2} (2 x) cot (2 x) - 2 csc^{2} (2 x) tan (2 x)

= \frac{2 sec ^{2} ( 2 x ) - 2 sec ^{2} ( 2 x ) cot ( 2 x ) - 2 csc ^{2} ( 2 x ) tan ( 2 x )}{- 2 cot ( 2 x ) + csc ^{2} ( 2 x )}

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

e x p an d \frac{10 x ( - 5 x ^{3} + y ^{3} )}{y ^{5}}

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

e x p an d \frac{d x}{x ( 4 - x )}

\frac{d ^{2}}{d x ^{2}} ((y) (x^{2} + y^{2} - 6 x - 8 y + 16))