(1-sin (x)**2)/(1+tan (x)**2)

cos(x)**4

solve((-sin(x)**2 + 1)/(tan(x)**2 + 1), x)

diff((-sin(x)**2 + 1)/(tan(x)**2 + 1), x)

series((-sin(x)**2 + 1)/(tan(x)**2 + 1), x, 0, 10)

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