how does (-1/144)cot(asin(x/12)) become (((-(x^2)/144)+1)^0.5)/(-12x) ??? with steps plz, thxxxxxxx?

Sol
[(－x^2/144)+1]^0.5/(－12x)
=12*[(－x^2/144)+1]^0.5/[12*(－12x)]
=[144*(－x^2/144)+1]^0.5/(－144x)
=(－1/144)*(－x^2+144)^0.5/x
=－√(144－x^2)/x
Set w=ArcSin(x/12)
Sinw=x/12
(1) x>=0
w在第一象限
Cotw=√(144－x^2)/x>0
(－1/144)Cot[ArcSin(x/12)]
=(－1/144)Cot(w)
=(－1/144)*√(144－x^2)/x
(2) x<0
w在第四象限
Cotw=√(144－x^2)/x<0
(－1/144)Cot[ArcSin(x/12)]
=(－1/144)Cot(w)
=(－1/144)*√(144－x^2)/x