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ioda
3 years ago
6

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

Mathematics
2 answers:
Anestetic [448]3 years ago
7 0

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)

SCORPION-xisa [38]3 years ago
3 0
<h2>Hello!</h2>

The answer is:

The simplified expression is:

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

<h2>Why?</h2>

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!

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