如何求sinx/ cosx？
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sinx = x -(1/6)x^3 +o(x^4)
cos(sinx)
= cos[x -(1/6)x^3 +o(x^4)]
= 1 - (1/2)[x -(1/6)x^3]^2 + (1/24)[x -(1/6)x^3]^4 +o(x^4)
= 1 - (1/2)[x^2 -(1/3)x^4 +o(x^4)]+ (1/24)[x^4+o(x^4)] +o(x^4)
=1- (1/2)x^2 + ( 1/6 +1/24) x^4 +o(x^4)
=1- (1/2)x^2 + (5/24) x^4 +o(x^4)
cos(sinx)
= cos[x -(1/6)x^3 +o(x^4)]
= 1 - (1/2)[x -(1/6)x^3]^2 + (1/24)[x -(1/6)x^3]^4 +o(x^4)
= 1 - (1/2)[x^2 -(1/3)x^4 +o(x^4)]+ (1/24)[x^4+o(x^4)] +o(x^4)
=1- (1/2)x^2 + ( 1/6 +1/24) x^4 +o(x^4)
=1- (1/2)x^2 + (5/24) x^4 +o(x^4)
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