Arctan Identities
There are various Arctan identities that are used to solve various trigonometric equations. Some of the important arctan identities are given below,
- arctan(-x) = -arctan(x), for all x ∈ R
- tan(arctan x) = x, for all real numbers x
- arctan (tan x) = x, for x ∈ (-π/2, π/2)
- arctan(1/x) = π/2 – arctan(x) = arccot(x), if x > 0
- arctan(1/x) = -π/2 – arctan(x) = arccot(x) – π, if x < 0
- sin(arctan x) = x/ √(1+x2)
- cos(arctan x) = 1/ √(1+x2)
- arctan(x) = 2arctan {x/(1 + √(1+x2))}
- arctan(x) = ∫ox 1/√(1+z2)dz
Arctan
Arctan is defined as the inverse of the tangent function. Arctan(x) is denoted as tan-1(x). There are six trigonometric functions and the inverse of all six functions is repressed as, sin-1x, cos-1x, tan-1x, cosec-1x, sec-1x, and cot-1x.
Arctan (tan-1x) is not similar to 1 / tan x. tan-1 x is the inverse of tan x whereas 1/ tan x is the reciprocal of tan x. tan-1 x is used to solve various trigonometric equations. In this article, we will study the arctan function formula, graph, properties, and others in detail.
Table of Content
- What is Arctan?
- What is Arctan Formula?
- Arctan Identities
- Arctan Domain and Range
- Arctan (x) Properties
- Arctan Table