1╱sinx的平方-cosx的平方╱x的平方.当x趋于0时,求极限

原式=limx→0 (x^2-sin^2xcos^2x)/x^2sin^2x
=limx→0 (4x^2-sin^22x)/4x^4 (sinx~x)
=limx→0 (8x-2sin2xcos2x*2)/16x^3
=limx→0 (4x-sin4x)/8x^3
=limx→0 (4-4cos4x)/24x^2
=limx→0 (1-cos4x)/6x^2
=limx→0 sin^2(2x)/3x^2
=limx→0 (2x)^2/3x^2 (sin2x~2x)
=4/3.