vereinfachen 2(sin(x)cos(x)-cos^2(x))+cos(2x)+sin(2x)

Lösung

vereinfachen

2 (sin (x) cos (x) - cos^{2} (x)) + cos (2 x) + sin (2 x)

cos (2 x) + 2 sin (2 x) - 2 cos^{2} (x)

Schritte zur Lösung

2 (sin (x) cos (x) - cos^{2} (x)) + cos (2 x) + sin (2 x)

Schreibe

2 (sin (x) cos (x) - cos^{2} (x))

um:

2 cos (x) sin (x) - 2 cos^{2} (x)

= 2 cos (x) sin (x) - 2 cos^{2} (x) + cos (2 x) + sin (2 x)

Verwende die Doppelwinkelidentität:

2 sin (x) cos (x) = sin (2 x)

= cos (2 x) + sin (2 x) + sin (2 x) - 2 cos^{2} (x)

Addiere gleiche Elemente:

sin (2 x) + sin (2 x) = 2 sin (2 x)

= cos (2 x) + 2 sin (2 x) - 2 cos^{2} (x)

e x p an d e^{x^{x}} x^{x} (ln (x) + 1) + e^{x^{x}} x^{2 x} (ln (x) + 1)

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

e x p an d \frac{1 - e ^{- x} + x ^{2} + 4 x}{x ( x ^{2} + 4 x + 5 )}

e x p an d c (8, 4) yD I (12, - 4)

s im pl i f y (i w + 1)^{2}