erweitern sin(x)cos(x)(csc(x)+tan(x))

Lösung

erweitern

sin (x) cos (x) (csc (x) + tan (x))

cot (x) sin (x) + sin^{2} (x)

Schritte zur Lösung

sin (x) cos (x) (csc (x) + tan (x))

= cos (x) sin (x) (csc (x) + tan (x))

Wende das Distributivgesetz an:

a (b + c) = ab + a c

cos (x) sin (x) (csc (x) + tan (x)) = cos (x) sin (x) csc (x) + cos (x) sin (x) tan (x)

= cos (x) sin (x) csc (x) + cos (x) sin (x) tan (x)

Vereinfache

cos (x) sin (x) csc (x) + cos (x) sin (x) tan (x) : sin (x) (cot (x) + sin (x))

= sin (x) (cot (x) + sin (x))

Wende das Distributivgesetz an:

a (b + c) = ab + a c

sin (x) (cot (x) + sin (x)) = sin (x) cot (x) + sin (x) sin (x)

= sin (x) cot (x) + sin (x) sin (x)

Vereinfache

sin (x) cot (x) + sin (x) sin (x) : cot (x) sin (x) + sin^{2} (x)

= cot (x) sin (x) + sin^{2} (x)

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

e x p an d (x + i y)^{3} - 2 (x + i y) + 6

e x p an d (x - 1 + i) (x - 1 - i)

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

e x p an d - \frac{8 ( - 3 x ^{2} - 4 )}{( x ^{2} - 4 ) ^{3}}