beweisen (1-sin(3a))(sin(3a)+1)=cos^2(3a)

Lösung

beweisen

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

Wahr

Schritte zur Lösung

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

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

(1 + sin (x)) (1 - sin (x))

Multipliziere aus

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

(1 + sin (x)) (1 - sin (x))

Wende Formel zur Differenz von zwei Quadraten an:

(a + b) (a - b) = a^{2} - b^{2}

a = 1, b = sin (x)

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

Wende Regel an

1^{a} = 1

1^{2} = 1

= 1 - sin^{2} (x)

= 1 - sin^{2} (x)

Verwende die Pythagoreische Identität:

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

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

= cos^{2} (x)

\Rightarrow Wahr

p ro v e \frac{sin ( x )}{1 + cos ( 2 x )} = tan (x)

p ro v e sec (t) (csc (t) (tan (t) + cot (t))) = sec^{2} (t) + csc^{2} (t)

p ro v e (1 + sin (x))^{2} + cos^{2} (x) = 2 + 2 sin (x)

p ro v e cot (6 0^{\circ}) = \frac{cos ( 6 0 ^{\circ} )}{sin ( 6 0 ^{\circ} )}

p ro v e tan (- x) tan (\frac{π}{2} - x) = - 1