1. **State the problem:** Solve the trigonometric identity or equation: $$\csc^4 x - \cot^4 x = \csc^2 x + \cot^2 x$$ 2. **Recall the Pythagorean identity:** We know that: $$\csc^2 x - \cot^2 x = 1$$ This is a fundamental identity relating cosecant and cotangent. 3. **Rewrite the left side as a difference of squares:** $$\csc^4 x - \cot^4 x = (\csc^2 x)^2 - (\cot^2 x)^2 = (\csc^2 x - \cot^2 x)(\csc^2 x + \cot^2 x)$$ 4. **Substitute the identity from step 2:** $$= 1 \cdot (\csc^2 x + \cot^2 x) = \csc^2 x + \cot^2 x$$ 5. **Compare with the right side:** The right side is exactly $$\csc^2 x + \cot^2 x$$. 6. **Conclusion:** The equation $$\csc^4 x - \cot^4 x = \csc^2 x + \cot^2 x$$ is an identity, meaning it holds true for all values of $$x$$ where the functions are defined. **Final answer:** The given equation is an identity and is true for all valid $$x$$.