erweitern sin^2(u)(v^2+1)+cos^2(u)(v^2+1)+v^2

Lösung

erweitern

sin^{2} (u) (v^{2} + 1) + cos^{2} (u) (v^{2} + 1) + v^{2}

v^{2} + v^{2} cos^{2} (u) + v^{2} sin^{2} (u) + 1

Schritte zur Lösung

sin^{2} (u) (v^{2} + 1) + cos^{2} (u) (v^{2} + 1) + v^{2}

Schreibe

sin^{2} (u) (v^{2} + 1)

um:

sin^{2} (u) v^{2} + sin^{2} (u)

= sin^{2} (u) v^{2} + sin^{2} (u) + cos^{2} (u) (v^{2} + 1) + v^{2}

Schreibe

cos^{2} (u) (v^{2} + 1)

um:

cos^{2} (u) v^{2} + cos^{2} (u)

= sin^{2} (u) v^{2} + sin^{2} (u) + cos^{2} (u) v^{2} + cos^{2} (u) + v^{2}

Verwende die Pythagoreische Identität:

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

= v^{2} + v^{2} cos^{2} (u) + v^{2} sin^{2} (u) + 1

e x p an d (\times + \frac{1}{2}) (x - \frac{1}{2})

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

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

e x p an d ((a + b F + c F^{2})^{2}) F^{2} \cdot (1 - d F - e F^{2})

e x p an d (tan (θ) + 1) (cos (θ) - 1)