sin^2(x)=1-2cos^2(x)

Lösung

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

x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn

Grad

x = 9 0^{\circ} + 36 0^{\circ} n, x = 27 0^{\circ} + 36 0^{\circ} n

Schritte zur Lösung

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

Subtrahiere

1 - 2 cos^{2} (x)

von beiden Seiten

sin^{2} (x) - 1 + 2 cos^{2} (x) = 0

Umschreiben mit Hilfe von Trigonometrie-Identitäten

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

Verwende die Pythagoreische Identität:

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

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

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

Vereinfache

= cos^{2} (x)

cos^{2} (x) = 0

Wende Regel an

x^{n} = 0 \Rightarrow x = 0

cos (x) = 0

Allgemeine Lösung für

cos (x) = 0

cos (x)

Periodizitätstabelle mit

2 πn

Zyklus:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn

x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn

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

3 + 8 cos (2 θ) = - 1

- 4 cos^{2} (x) + 6 cos (x) = 2

sec (θ) = - \frac{4}{3}

tan (2 x) = tan (201 8^{\circ})