tan^-1(x)
1/(1+x^2)
The function tan^-1(x) is the inverse function of the tangent function, which gives the angle whose tangent is x.
The range of tan^-1(x) is (-π/2, π/2), which means that its output is always within that range.
Graphically, the function y = tan^-1(x) is a curve that passes through (-1, -π/4), (0, 0), and (1, π/4) on the x-y plane.
The derivative of tan^-1(x) is 1/(1+x^2).
Some common trigonometric identities involving tan^-1(x) include:
– tan(tan^-1(x)) = x
– tan^-1(tan(x)) = x
– tan^-1(x) + tan^-1(1/x) = π/2 for x > 0
Overall, the function tan^-1(x) is a useful tool in solving trigonometric equations and in applications involving angles and their tangents.
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