A function in mathematics is a relationship between a set of inputs and their corresponding outputs. Each input is mapped to exactly one output. Functions are commonly represented by equations or graphs and are used to model real-world scenarios in fields such as physics, economics and engineering.
Class 12 Maths Chapter 2 Inverse Trigonometric Functions covers the inverse of trigonometric functions like sine and cosine and tangent or cosecant and secant and cotangent. It teaches how to determine angles when the value of a trigonometric function is given. The chapter includes domains ranges graphs and solving equations with inverse trigonometric functions.
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To solve the problem given, let’s go through the properties of the inverse tangent function:
Step 1: Define tan⁻¹x = y
The function tan⁻¹x = y is a tangent function inverse. The definition simply states that for any real number x, angle y is such that:tan(y) = x
Step 2: Range of tan⁻¹x
The principal range of the inverse tangent function tan⁻¹x (or arctan) is:
-π/2 ≤ y ≤ π/2
This signifies that y is in the interval (-π/2, π/2).
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