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Low order Taylor expansion

When I try to Taylor expand the following expression

f(x) = sin(x)^6 / ( 8 - 15cos(x) + 10cos(x)^3 - 3*cos(x)^5)

up to a low order like 4, sage returns 0, but for higher orders like 6 and up, it correctly Taylor expands the function but it suddenly also finds lower order terms. the following code shows the issue

[taylor(f(x), x, 0, i) for i in range(8) ]

the first 5 expansions give 0, from order 6 on, sage finds also lower order terms.

Low order Taylor expansion

When I try to Taylor expand the following expression

f(x) = sin(x)^6 / ( 8 - 15cos(x) 15*cos(x) + 10cos(x)^3 10*cos(x)^3 - 3*cos(x)^5)

3*cos(x)^5)

up to a low order like 4, sage returns 0, but for higher orders like 6 and up, it correctly Taylor expands the function but it suddenly also finds lower order terms. the following code shows the issue

[taylor(f(x), x, 0, i) for i in range(8) ]

]

the first 5 expansions give 0, from order 6 on, sage finds also lower order terms.