erweitern cos(x)(1+tan(x))(1-tan(x))

Lösung

erweitern

cos (x) (1 + tan (x)) (1 - tan (x))

cos (2 x) sec (x)

Schritte zur Lösung

cos (x) (1 + tan (x)) (1 - tan (x))

Schreibe

cos (x) (1 + tan (x)) (1 - tan (x))

um:

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

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

Wende das Distributivgesetz an:

a (b - c) = ab - a c

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

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

Vereinfache

cos (x) \cdot 1 - cos (x) tan^{2} (x) : cos (2 x) sec (x)

= cos (2 x) sec (x)

e x p an d (\frac{1}{2} n - 2 v)^{10}

e x p an d \frac{- x ^{2} + 2 x + 8}{( x ^{2} + 3 x + 5 ) ^{2}}

e x p an d \frac{- 3 + 2 s}{s ^{2} ( s ^{2} - 9 )}

e x p an d (x^{2} - \frac{2}{x})^{10}

e x p an d - π sin (π t) cos (π t) + e^{t} (3 e^{t} + 7)