Question: 81 sin² x + 81 cos² x = 30
0 ≤ x ≤ 360°
1. **State the problem:**
Solve the equation $$81 \sin^2 x + 81 \cos^2 x = 30$$ for $$x$$ in the interval $$0 \leq x \leq 360^\circ$$.
2. **Recall the Pythagorean identity:**
We know that $$\sin^2 x + \cos^2 x = 1$$ for all $$x$$.
3. **Apply the identity to the equation:**
Substitute $$\sin^2 x + \cos^2 x = 1$$ into the equation:
$$
81 (\sin^2 x + \cos^2 x) = 30
$$
which simplifies to
$$
81 \times 1 = 30
$$
4. **Simplify the equation:**
$$
81 = 30
$$
5. **Analyze the result:**
This is a contradiction because $$81 \neq 30$$.
6. **Conclusion:**
There is no value of $$x$$ in $$0 \leq x \leq 360^\circ$$ that satisfies the equation.
**Final answer:** No solution.