erweitern (3sin(x)+cos(x))^2

Lösung

erweitern

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

9 sin^{2} (x) + 6 cos (x) sin (x) + cos^{2} (x)

Schritte zur Lösung

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

Wende Formel für perfekte quadratische Gleichungen an:

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

(3 sin (x) + cos (x))^{2} = (3 sin (x))^{2} + 2 \cdot 3 sin (x) cos (x) + cos^{2} (x)

= (3 sin (x))^{2} + 2 \cdot 3 sin (x) cos (x) + cos^{2} (x)

Vereinfache

(3 sin (x))^{2} + 2 \cdot 3 sin (x) cos (x) + cos^{2} (x) : 9 sin^{2} (x) + 6 cos (x) sin (x) + cos^{2} (x)

= 9 sin^{2} (x) + 6 cos (x) sin (x) + cos^{2} (x)

e x p an d (tan (4 x) - tan (x)) \cdot (cos (5 x) + cos (3 x))

e x p an d \frac{2 x ( x ^{2} - 12 )}{( x ^{2} + 4 ) ^{3}}

s im pl i f y (1 + 2 i)^{10}

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

e x p an d (x + 1)!