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

Question

contestada

Respuesta :

luisejr77 luisejr77 · Answer 1 · 2019-05-02T04:49:34+02:00

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]

mixter17 mixter17 · Answer 2 · 2019-05-02T05:01:30+02:00

The answer is:

The simplified expression is:

[tex]Sin(-x)*Cos(-x)*Csc(-x)=Cos(x)[/tex]

To simplify the expression we need to use the following trigonometric identities:

[tex]Sin(-x)=-Sin(x)\\Cos(-x)=Cos(x)\\Csc(-x)=-Csc(x)\\Csc(x)=\frac{1}{Sin(x)}[/tex]

We are given the expression:

[tex]sin(-x)*cos(-x)*csc(-x)[/tex]

So, applying the identities and simplifying, we have:

[tex]Sin(-x)*Cos(-x)*Csc(-x)=-Sin(x)*Cos(x)*-\frac{1}{Sin(x)}[/tex]

[tex]Sin(-x)*Cos(-x)*Csc(-x)=Cos(x)*-Sin(x)*-\frac{1}{Sin(x)}[/tex]

[tex]Sin(-x)*Cos(-x)*Csc(-x)=Cos(x)[/tex]

Hence, the simplified expression is:

[tex]Sin(-x)*Cos(-x)*Csc(-x)=Cos(x)[/tex]

Have a nice day!