Answer in 60

Answered By: Henry Cooper Date: created: Dec 29 2021

Input

tan(x - π/2)

Result

-cot(x)

Alternate forms

-cos(x)/sin(x)

Alternate form assuming x is real

sin(2 x)/(cos(2 x) - 1)

Roots

x = 1/2 (2 π n + π), n element Z

Series expansion at x=0

-1/x + x/3 + x^3/45 + (2 x^5)/945 + O(x^6)(Laurent series)

Derivative

d/dx(tan(x - π/2)) = csc^2(x)

Indefinite integral

integral-cot(x) dx = -log(sin(x)) + constant(assuming a complex-valued logarithm)

Addition formulas

tan(x - π/2) = (tan(-π/2) + tan(x))/(1 - tan(-π/2) tan(x))

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