展开 (1-(1-cos(xpi))/2)10^{x/2}

解答

展开

(1 - \frac{1 - cos ( x π )}{2}) 1 0^{\frac{x}{2}}

1 0^{\frac{x}{2}} - 2^{\frac{x - 2}{2}} \cdot 5^{\frac{x}{2}} + 2^{\frac{x - 2}{2}} \cdot 5^{\frac{x}{2}} cos (π x)

求解步骤

(1 - \frac{1 - cos ( x π )}{2}) \cdot 1 0^{\frac{x}{2}}

= 1 0^{\frac{x}{2}} (1 - \frac{1 - cos ( π x )}{2})

使用分配律:

a (b - c) = ab - a c

a = 1 0^{\frac{x}{2}}, b = 1, c = \frac{1 - cos ( x π )}{2}

= 1 0^{\frac{x}{2}} \cdot 1 - 1 0^{\frac{x}{2}} \cdot \frac{1 - cos ( x π )}{2}

= 1 \cdot 1 0^{\frac{x}{2}} - 1 0^{\frac{x}{2}} \cdot \frac{1 - cos ( π x )}{2}

化简

1 \cdot 1 0^{\frac{x}{2}} - 1 0^{\frac{x}{2}} \cdot \frac{1 - cos ( π x )}{2} : 1 0^{\frac{x}{2}} - 2^{\frac{x - 2}{2}} \cdot 5^{\frac{x}{2}} + 2^{\frac{x - 2}{2}} \cdot 5^{\frac{x}{2}} cos (π x)

= 1 0^{\frac{x}{2}} - 2^{\frac{x - 2}{2}} \cdot 5^{\frac{x}{2}} + 2^{\frac{x - 2}{2}} \cdot 5^{\frac{x}{2}} cos (π x)

e x p an d \frac{1}{8} e^{4 x} (- 4 e^{- 4 t} t - e^{- 4 t})

e x p an d 2 cos (5) (2 tan (5) x + 25)

e x p an d y^{2} d x + (x^{2} + x y) d y

e x p an d sin (θ) - cos (θ) (sin (θ) - cos (θ))

s im pl i f y (i + 2)^{4}