Use basic trigonometric identities to simplify the expression: sin (-x) cos (-x) csc (-x) =?

Answer:[tex]sin (-x) cos (-x) csc (-x) =cos(x)[/tex]Step-by-step explanation:We know by definition that the cosine is an even function, therefore[tex]cos (-x) = cos (x)[/tex]We also know that the sin is an odd function, therefore[tex]sin (-x) = -sin (x)[/tex]By definition:[tex]cscx = \frac{1}{sinx}.[/tex]Then:[tex]csc(-x) = \frac{1}{sin(-x)}.[/tex][tex]csc(-x) = -\frac{1}{sin(x)}.[/tex]Using these trigonometric properties we can simplify the expression[tex]sin (-x) cos (-x) csc (-x)= -sin(x)cos(x)*(-\frac{1}{sin(x)})\\\\sin (-x) cos (-x) csc (-x)=cos(x)[/tex]