cos(270+ theeta) / sin ( theeta+ 270)= - sin theeta/ cos theeta

Let's analyze the expression and simplify it step by step.

Given:
\[
\frac{\cos(270^\circ + \theta)}{\sin(\theta + 270^\circ)} = -\frac{\sin \theta}{\cos \theta}
\]

### Step 1: Simplify \(\cos(270^\circ + \theta)\)

Using the trigonometric identity:
\[
\cos(270^\circ + \theta) = \sin(\theta)
\]

So, the numerator becomes:
\[
\cos(270^\circ + \theta) = \sin(\theta)
\]

### Step

Learn how to solve the trigonometric identity cos(270 + θ) / sin(θ + 270) = -sin θ / cos θ with a step-by-step explanation. This problem involves advanced trigonometric concepts and identities. Suitable for advanced high school or college-level students.

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