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(1+tan(x))^2+(1-tan(x))^2=sec^2(x)

Lösung

(1 + tan (x))^{2} + (1 - tan (x))^{2} = sec^{2} (x)

Keine L \overset{o}{¨} sung f \overset{u}{¨} r x \in R

Schritte zur Lösung

(1 + tan (x))^{2} + (1 - tan (x))^{2} = sec^{2} (x)

Subtrahiere

sec^{2} (x)

von beiden Seiten

2 tan^{2} (x) - sec^{2} (x) + 2 = 0

Umschreiben mit Hilfe von Trigonometrie-Identitäten

2 - sec^{2} (x) + 2 tan^{2} (x)

Verwende die Pythagoreische Identität:

tan^{2} (x) + 1 = sec^{2} (x)

tan^{2} (x) = sec^{2} (x) - 1

= 2 - sec^{2} (x) + 2 (sec^{2} (x) - 1)

Vereinfache

2 - sec^{2} (x) + 2 (sec^{2} (x) - 1) : sec^{2} (x)

2 - sec^{2} (x) + 2 (sec^{2} (x) - 1)

Multipliziere aus

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

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

Wende das Distributivgesetz an:

a (b - c) = ab - a c

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

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

Multipliziere die Zahlen:

2 \cdot 1 = 2

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

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

Vereinfache

2 - sec^{2} (x) + 2 sec^{2} (x) - 2 : sec^{2} (x)

2 - sec^{2} (x) + 2 sec^{2} (x) - 2

Addiere gleiche Elemente:

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

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

Fasse gleiche Terme zusammen

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

2 - 2 = 0

= sec^{2} (x)

= sec^{2} (x)

= sec^{2} (x)

sec^{2} (x) = 0

Wende Regel an

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

sec (x) = 0

sec (x) \leq - 1 or sec (x) \geq 1

Keine L \overset{o}{¨} sung f \overset{u}{¨} r x \in R

tan (x) = - \frac{2}{2}

cot (x) = 1.2

tan (x) = \frac{30}{100}

sec (x) - tan (x) = 2

sin (\frac{2 π ( t + 101.75 )}{365}) = - 1