erweitern (sin(a/2)-cos(a/2))^2

Lösung

erweitern

(sin (\frac{a}{2}) - cos (\frac{a}{2}))^{2}

- sin (2 \cdot \frac{a}{2}) + 1

Schritte zur Lösung

(sin (\frac{a}{2}) - cos (\frac{a}{2}))^{2}

Wende Formel für perfekte quadratische Gleichungen an:

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

(sin (\frac{a}{2}) - cos (\frac{a}{2}))^{2} = sin^{2} (\frac{a}{2}) - 2 sin (\frac{a}{2}) cos (\frac{a}{2}) + cos^{2} (\frac{a}{2})

= sin^{2} (\frac{a}{2}) - 2 sin (\frac{a}{2}) cos (\frac{a}{2}) + cos^{2} (\frac{a}{2})

Vereinfache

sin^{2} (\frac{a}{2}) - 2 sin (\frac{a}{2}) cos (\frac{a}{2}) + cos^{2} (\frac{a}{2}) : - sin (2 \cdot \frac{a}{2}) + 1

= - sin (2 \cdot \frac{a}{2}) + 1

e x p an d \frac{5 ( x ^{2} + 4 )}{( x ^{2} - 49 ) ^{9}}

s im pl i f y (t - i t^{2})^{2}

e x p an d 5 (15 + 22 e^{\frac{4 l n ( \frac{15}{22} )}{3}})

e x p an d (y^{4} + 8 x y^{4} - x^{3}) d x + (4 x y^{3} + 16 x^{2} y^{3}) d y

s im pl i f y (y - \frac{1}{3}) (y - \frac{2}{3})