vereinfachen (cos(x)+sec(x))^2+sin^2(x)-tan^2(x)+3

Lösung

vereinfachen

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

7

Schritte zur Lösung

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

Schreibe

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

um:

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

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

Verwende die Pythagoreische Identität:

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

= sec^{2} (x) + 2 cos (x) sec (x) - tan^{2} (x) + 3 + 1

Addiere die Zahlen:

3 + 1 = 4

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

Verwende die Pythagoreische Identität:

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

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

= 2 cos (x) sec (x) + 4 + 1

Addiere die Zahlen:

4 + 1 = 5

= 2 cos (x) sec (x) + 5

sec (x) cos (x) = 1

= 5 + 2 \cdot 1

Multipliziere die Zahlen:

2 \cdot 1 = 2

= 5 + 2

Addiere die Zahlen:

5 + 2 = 7

= 7

e x p an d (\frac{1}{2} - \frac{3}{2} i)^{16}

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

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

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

s im pl i f y (x - 3)^{2} (x - 7)