Question

高等数学 数学高手帮帮忙………… 求证√(1+tanX)-√(1+sinX)~1/4X^n

Answer 1

(1+tanx)^{-1/2}-(1+sinx)^{-1/2}
= (tanx - sinx) / [(1+tanx)^{1/2}+(1+sinx)^{1/2}]
= tanx * 2sin^2(x/2) / [(1+tanx)^{1/2}+(1+sinx)^{1/2}]
1/4 * x^3