erweitern (1+sin(x))^2-cos^2(x)

Lösung

erweitern

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

1 + 2 sin (x) + sin^{2} (x) - cos^{2} (x)

Schritte zur Lösung

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

Wende Formel für perfekte quadratische Gleichungen an:

(a + b)^{2} = a^{2} + 2 ab + b^{2}

(1 + sin (x))^{2} = 1^{2} + 2 \cdot 1 \cdot sin (x) + sin^{2} (x)

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

Vereinfache

1^{2} + 2 \cdot 1 \cdot sin (x) + sin^{2} (x) : 1 + 2 sin (x) + sin^{2} (x)

= 1 + 2 sin (x) + sin^{2} (x) - cos^{2} (x)

e x p an d (1 + \frac{x}{1 + \frac{x}{y}}) (x + y)

e x p an d \frac{3 ( 9 - y )}{2}

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

e x p an d \frac{- s ^{3} + 2 s ^{2} + 1}{s ^{2} ( s ^{2} + 1 )}

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