\(cos^{-1}(\frac{2sin^{-1}(\frac{1}{4x^2-1})}{π})\) is:
- \(R-\left\{{-\frac{1}{2},\frac{1}{2}}\right\}\)
- \((-∞,-1] ∪[1,∞)∪\left\{{0}\right\}\)
- \((-∞,\frac{-1}{2}] ∪[\frac{1}{2},∞)∪\left\{{0}\right\}\)
- \((-∞,\frac{-1}{\sqrt2}] ∪[\frac{1}{\sqrt2},∞)∪\left\{{0}\right\}\)
The Correct Option is D
Solution and Explanation
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Concepts Used:
Types of Differential Equations
There are various types of Differential Equation, such as:
Ordinary Differential Equations:
Ordinary Differential Equations is an equation that indicates the relation of having one independent variable x, and one dependent variable y, along with some of its other derivatives.
\(F(\frac{dy}{dt},y,t) = 0\)
Partial Differential Equations:
A partial differential equation is a type, in which the equation carries many unknown variables with their partial derivatives.
Linear Differential Equations:
It is the linear polynomial equation in which derivatives of different variables exist. Linear Partial Differential Equation derivatives are partial and function is dependent on the variable.
Homogeneous Differential Equations:
When the degree of f(x,y) and g(x,y) is the same, it is known to be a homogeneous differential equation.
\(\frac{dy}{dx} = \frac{a_1x + b_1y + c_1}{a_2x + b_2y + c_2}\)
Read More: Differential Equations