Question

solve.

\\\frac{\cos(-x)}{\sin x}\\

?

Explanation:

⚡ Using what you learned: Trigonometric Identities

Step 1: Apply the even-odd identity for cosine

The cosine function is an even function, which means:

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

Substituting this into the numerator of the expression gives:

$$ \frac{\cos(x)}{\sin(x)} $$

Step 2: Simplify using the cotangent identity

Using the quotient identity for cotangent:

$$ \frac{\cos(x)}{\sin(x)} = \cot(x) $$

Answer:

$$ \cot x $$