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Beliebt Algebra >

vereinfachen (tan(x)-sin(x))^2+(1-cos(x))^2

Lösung

vereinfachen

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

Lösung

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

Schritte zur Lösung

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

Schreibe

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

um:

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

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

Schreibe

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

um:

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

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

Verwende die Pythagoreische Identität:

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

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

Addiere die Zahlen:

1 + 1 = 2

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

Beliebte Beispiele

erweitern sin(0)

e x p an d sin (0)

erweitern 3cos(pi(x-1))

e x p an d 3 cos (π (x - 1))

erweitern ((x^2-1)^2)/(4x^2)

e x p an d \frac{( x ^{2} - 1 ) ^{2}}{4 x ^{2}}

erweitern (a^{1/2}-b^{1/2})(a^{1/2}+b^{1/2})

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

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

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