erweitern (1+sin(θ))^2sec^2(θ)

Lösung

erweitern

(1 + sin (θ))^{2} sec^{2} (θ)

sec^{2} (θ) + 2 sec^{2} (θ) sin (θ) + sec^{2} (θ) sin^{2} (θ)

Schritte zur Lösung

(1 + sin (θ))^{2} sec^{2} (θ)

= sec^{2} (θ) (1 + sin (θ))^{2}

Schreibe

(1 + sin (θ))^{2}

um:

1 + 2 sin (θ) + sin^{2} (θ)

= sec^{2} (θ) (1 + 2 sin (θ) + sin^{2} (θ))

Wende das Distributivgesetz an:

m (a + b + c) = ma + mb + m c

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

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

Vereinfache

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

= sec^{2} (θ) + 2 sec^{2} (θ) sin (θ) + sec^{2} (θ) sin^{2} (θ)

e x p an d (csc (θ) + sec (θ))^{2}

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

e x p an d 9 z^{2} (4 e + 7 f) + 4 e + 7 f

e x p an d (5 a + b^{5}) l e f t (5 a - b^{5})

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