化简 1/2 (arcsin(x-1)+1/2 sin(2arcsin(x-1)))

解答

化简

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

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

求解步骤

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

使用分式法则:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

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

使用法则:

1 \cdot a = a

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

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

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

e x p an d \frac{7 s + 33}{s ( s ^{2} - 2 s + 17 )}

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

e x p an d (e^{8 x} + 2)^{2}

e x p an d - \frac{2 ( e ^{15} - 1 )}{3}