Question

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

Answer 1

Answer:

$sin (-x) cos (-x) csc (-x) =cos(x)$

Step-by-step explanation:

We know by definition that the cosine is an even function, therefore

$cos (-x) = cos (x)$

We also know that the sin is an odd function, therefore

$sin (-x) = -sin (x)$

By definition:

$cscx = \frac{1}{sinx}.$

Then:

$csc(-x) = \frac{1}{sin(-x)}.$

$csc(-x) = -\frac{1}{sin(x)}.$

Using these trigonometric properties we can simplify the expression

$sin (-x) cos (-x) csc (-x)= -sin(x)cos(x)*(-\frac{1}{sin(x)})\\\\sin (-x) cos (-x) csc (-x)=cos(x)$

Answer 2

Hello!

The answer is:

The simplified expression is:

$Sin(-x)*Cos(-x)*Csc(-x)=Cos(x)$

Why?

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

$Sin(-x)=-Sin(x)\\Cos(-x)=Cos(x)\\Csc(-x)=-Csc(x)\\Csc(x)=\frac{1}{Sin(x)}$

We are given the expression:

$sin(-x)*cos(-x)*csc(-x)$

So, applying the identities and simplifying, we have:

$Sin(-x)*Cos(-x)*Csc(-x)=-Sin(x)*Cos(x)*-\frac{1}{Sin(x)}$

$Sin(-x)*Cos(-x)*Csc(-x)=Cos(x)*-Sin(x)*-\frac{1}{Sin(x)}$

$Sin(-x)*Cos(-x)*Csc(-x)=Cos(x)$

Hence, the simplified expression is:

$Sin(-x)*Cos(-x)*Csc(-x)=Cos(x)$

Have a nice day!