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Beliebt Algebra >

vereinfachen (sin(x)-cos(x))(cos(x)-sin(x))

Lösung

vereinfachen

(sin (x) - cos (x)) (cos (x) - sin (x))

Lösung

sin (2 x) - 1

Schritte zur Lösung

(sin (x) - cos (x)) (cos (x) - sin (x))

Vereinfache

cos (x) - sin (x) : - (sin (x) - cos (x))

= (sin (x) - cos (x)) (- (sin (x) - cos (x)))

Apply rule:

a (- b) = - ab

(sin (x) - cos (x)) (- (sin (x) - cos (x))) = - (sin (x) - cos (x)) (sin (x) - cos (x))

= - (sin (x) - cos (x)) (sin (x) - cos (x))

Wende Exponentenregel an:

aa = a^{2}

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

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

Vereinfache

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

= - (- sin (2 x) + 1)

Wende das Distributivgesetz an:

- (- a + b) = a - b

- (- sin (2 x) + 1) = sin (2 x) - 1

= sin (2 x) - 1

Beliebte Beispiele

erweitern (3x-sqrt(3))^4

e x p an d (3 x - 3)^{4}

erweitern (0.1(s+1)(s+30.1))/s

e x p an d \frac{0.1 ( s + 1 ) ( s + 30.1 )}{s}

erweitern ((x+1)^2)/2

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

erweitern (3/2 , 5/4)y(1/2 ,-3/4)

e x p an d (\frac{3}{2}, \frac{5}{4}) y (\frac{1}{2}, - \frac{3}{4})

erweitern (x-1)/(x^2(x-2)^3)

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