展开 (sin(x/2)+cos(x/2))^2-sin(x)

解答

展开

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

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

求解步骤

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

使用完全平方公式:

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

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

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

化简

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

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

s im pl i f y (x + 3 - 23) (x + 3 + 23)

s im pl i f y (z - \frac{1}{2}) (z - \frac{1}{5})

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

e x p an d \frac{25}{( t + 1 ) ^{2}}

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