Question

simplify.

\\(\sin(-x)\csc x\\)

Explanation:

⚡ Using what you learned: Trigonometric Identities

Step 1: Apply the odd-even identity

The sine function is an odd function, which means:

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

Substituting this into the expression:

$$ -\sin(x) \csc(x) $$

Step 2: Apply the reciprocal identity

The cosecant function is the reciprocal of the sine function:

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

Substituting this into the expression:

$$ -\sin(x) \cdot \frac{1}{\sin(x)} $$

Step 3: Simplify the expression

Cancel out the common factor \( \sin(x) \):

$$ -1 $$

Answer:

-1