Question

are x^2-1 and tanx=sinx/cosx rational expressions?

Answer 1

x^{2} -1 is a rational expression but tanx= sinx/ cos x is not a rational expression

Rational expressions are fractions where numerator and denominator are polynomials. x^{2} -1 can be written as 

{x^{2}-1}/ 1. Here x^{2} -1 and 1 both are polynomials. Therefore x^{2} -1 is a rational expression.

tanx , sinx and cosx are trigonometric functions and therefore they are not polynomials.