1. The problem is to simplify or solve an expression involving $\cos 70^\circ$, $\cos 20^\circ$, and $\cos 25^\circ$ without directly knowing their values. 2. We use trigonometric identities and angle sum/difference formulas to rewrite expressions involving cosines of angles. 3. Recall the cosine addition and subtraction formulas: $$\cos(a \pm b) = \cos a \cos b \mp \sin a \sin b$$ 4. Also, use the fact that $\cos(90^\circ - \theta) = \sin \theta$. 5. For example, $\cos 70^\circ = \sin 20^\circ$ because $70^\circ = 90^\circ - 20^\circ$. 6. Similarly, $\cos 25^\circ$ and $\cos 20^\circ$ can be related using sum and difference identities or complementary angles. 7. By expressing all cosines in terms of sines or using sum-to-product formulas, we can simplify the expression without knowing the exact values. 8. For instance, the sum-to-product formula: $$\cos A + \cos B = 2 \cos \frac{A+B}{2} \cos \frac{A-B}{2}$$ 9. Applying these identities step-by-step allows simplification without numerical values. Final answer: The expression can be simplified using trigonometric identities such as sum-to-product and complementary angle relationships without knowing the exact values of $\cos 70^\circ$, $\cos 20^\circ$, and $\cos 25^\circ$.