Show that between any two roots of `e^(x) cos x=1`, there exists at least one root of `e^(x) sin x-1=0`

Show that between any two roots of e^(-x)-cos x=0, there exists at least one root of sin x-e^(-x)=0

Which of the following is/are correct? Between any two roots of e^xcosx=1, there exists at least one root of tanx=1. Between any two roots of e^xsinx=1, there exists at least one root of tanx=-1. Between any two roots of e^xcosx=1, there exists at least one root of e^xsinx=1. Between any two roots of e^xsinx=1, there exists at least one root of e^xcosx=1.

In between any two real roots of an e^(x)sin x=1 there exists how many roots satisfying equation e^(x)cos x=-1

The equation sin x+x cos x=0 has at least one root in

Statement-1: The equation e^(x-1) +x-2=0 has only one real root. Statement-2 : Between any two root of an equation f(x)=0 there is a root of its derivative f'(x)=0

Statement -1 : one root of the equation x^(2)+5x-7=0 lie in the interval (1,2). and Statement -2 : For a polynomial f(x),if f(p)f(q) lt 0, then there exists at least one real root of f(x) =0 in (p,q)

Between any two real roots of the equation e^(x)sinx-1=0 the equation e^(x)cosx+1=0 has

Let a and b be two distinct roots of a polynomial equation f(x) =0 Then there exist at least one root lying between a and b of the polynomial equation