English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

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

Lösung

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

x = 2 πn, x = π + 2 πn

Grad

x = 0^{\circ} + 36 0^{\circ} n, x = 18 0^{\circ} + 36 0^{\circ} n

Schritte zur Lösung

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

Subtrahiere

2

von beiden Seiten

2 cos^{2} (x) + 3 sin^{2} (x) - 2 = 0

Umschreiben mit Hilfe von Trigonometrie-Identitäten

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

Verwende die Pythagoreische Identität:

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

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

= - 2 + 2 (1 - sin^{2} (x)) + 3 sin^{2} (x)

Vereinfache

- 2 + 2 (1 - sin^{2} (x)) + 3 sin^{2} (x) : sin^{2} (x)

- 2 + 2 (1 - sin^{2} (x)) + 3 sin^{2} (x)

Multipliziere aus

2 (1 - sin^{2} (x)) : 2 - 2 sin^{2} (x)

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

Wende das Distributivgesetz an:

a (b - c) = ab - a c

a = 2, b = 1, c = sin^{2} (x)

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

Multipliziere die Zahlen:

2 \cdot 1 = 2

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

= - 2 + 2 - 2 sin^{2} (x) + 3 sin^{2} (x)

Vereinfache

- 2 + 2 - 2 sin^{2} (x) + 3 sin^{2} (x) : sin^{2} (x)

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

Addiere gleiche Elemente:

- 2 sin^{2} (x) + 3 sin^{2} (x) = sin^{2} (x)

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

- 2 + 2 = 0

= sin^{2} (x)

= sin^{2} (x)

= sin^{2} (x)

sin^{2} (x) = 0

Wende Regel an

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

sin (x) = 0

Allgemeine Lösung für

sin (x) = 0

sin (x)

Periodizitätstabelle mit

2 πn

Zyklus:

x = 0 + 2 πn, x = π + 2 πn

x = 0 + 2 πn, x = π + 2 πn

Löse

x = 0 + 2 πn : x = 2 πn

x = 0 + 2 πn

0 + 2 πn = 2 πn

x = 2 πn

x = 2 πn, x = π + 2 πn

42 - 25 cos (x) = 31

2 sec^{2} (x) = 5 tan (x)

cos^{2} (2 x) - 3 sin^{2} (x) - 1 = 0

sin (- t) = \frac{3}{10}

cos^{2} (x) + sin^{3} (x) = 0