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`

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

Between any two real roots of the equation e^xsinx-1=0 , the equation e^xcosx+1=0 has :

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

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

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

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

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

Between any two real roots of the equation e^(x) sin x =1 , the equation e^(x) cos x = -1 has

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.