erweitern (1-tan^2(x))(1-tan^2(2x))tan(4x)

Lösung

erweitern

(1 - tan^{2} (x)) (1 - tan^{2} (2 x)) tan (4 x)

tan (4 x) - tan^{2} (2 x) tan (4 x) - tan^{2} (x) tan (4 x) + tan^{2} (x) tan^{2} (2 x) tan (4 x)

Schritte zur Lösung

(1 - tan^{2} (x)) (1 - tan^{2} (2 x)) tan (4 x)

= tan (4 x) (1 - tan^{2} (x)) (1 - tan^{2} (2 x))

Apply FOIL method

(1 - tan^{2} (x)) (1 - tan^{2} (2 x)) : 1 - tan^{2} (2 x) - tan^{2} (x) + tan^{2} (x) tan^{2} (2 x)

= tan (4 x) (1 - tan^{2} (2 x) - tan^{2} (x) + tan^{2} (x) tan^{2} (2 x))

Setze Klammern

= tan (4 x) \cdot 1 + tan (4 x) (- tan^{2} (2 x)) + tan (4 x) (- tan^{2} (x)) + tan (4 x) tan^{2} (x) tan^{2} (2 x)

Vereinfache

tan (4 x) \cdot 1 + tan (4 x) (- tan^{2} (2 x)) + tan (4 x) (- tan^{2} (x)) + tan (4 x) tan^{2} (x) tan^{2} (2 x) : tan (4 x) - tan^{2} (2 x) tan (4 x) - tan^{2} (x) tan (4 x) + tan^{2} (x) tan^{2} (2 x) tan (4 x)

= tan (4 x) - tan^{2} (2 x) tan (4 x) - tan^{2} (x) tan (4 x) + tan^{2} (x) tan^{2} (2 x) tan (4 x)

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