\( \begin{array}{ll}\text { (3) } \frac{\cos ^{2} 165^{\circ}}{\cos 60^{\circ}}-\cos ^{2} 97^{\circ}-\cos ^{2} 727^{\circ} & \text { (4) } \frac{\cos 204^{\circ} \tan 315^{\circ}+2 \cos 156^{\circ} \sin ^{2} 348}{\sin ^{2}\left(-5^{\circ}\right)+\sin ^{2} 85^{\circ}-\sin ^{2} 24^{\circ}} \\ \text { (5) } \sin 140^{\circ}-\cos 220^{\circ} \tan \left(-155^{\circ}\right) & \text { (6) } \frac{\cos ^{4} 190^{\circ}-\sin ^{4}\left(-10^{\circ}\right)}{\cos 55^{\circ} \cos 325^{\circ}}\end{array} \)

We will simplify each of the four expressions step‐by‐step. ───────────────────────────── Step (3): Evaluate   [cos²(165°)]⁄[cos(60°)] – cos²(97°) – cos²(727°). 1. Notice that cos 60° = ½ so   cos²(165°)/cos60° = cos²(165°)/(½) = 2·cos²(165°). 2. Write the angles in terms of acute angles:  • 165° = 180° – 15° ⟹ cos(165°) = –cos15° ⟹ cos²(165°) = cos²15°.  • 97° = 90° + 7°  ⟹ cos(97°) = –sin7° ⟹ cos²(97°) = sin²7°.  • 727° differs by full rotations. Since 727° – 720° = 7°, we have   cos²(727°) = cos²7°. 3. The expression becomes:   2·cos²15° – sin²7° – cos²7°.  But recall that sin²7° + cos²7° = 1.  Thus, the expression is 2·cos²15° – 1. 4. Recognize the double‐angle formula:   2·cos²15° – 1 = cos30°.  Since cos30° = (√3)/2, the final answer for (3) is (√3)/2. ───────────────────────────── Step (4): Evaluate   [cos(204°)·tan(315°) + 2·cos(156°)·sin²(348°)] ÷ [sin²(–5°) + sin²(85°) – sin²(24°)]. Numerator: 1. For cos(204°): 204° = 180° + 24° so cos(204°) = –cos24°. 2. For tan(315°): 315° = 360° – 45° so tan(315°) = –tan45° = –1.  Then, cos(204°)·tan(315°) = (–cos24°)(–1) = cos24°. 3. For cos(156°): 156° = 180° – 24° so cos(156°) = –cos24°. 4. For sin(348°): 348° = 360° – 12° so sin(348°) = –sin12°, and sin²(348°) = sin²12°.  Then, 2·cos(156°)·sin²(348°) = 2·(–cos24°)·sin²12° = –2·cos24°·sin²12°. 5. The entire numerator becomes:   cos24° – 2·cos24°·sin²12° = cos24°·(1 – 2 sin²12°). 6. Recognize that 1 – 2 sin²x = cos(2x). Here, with x = 12°, we have:   1 – 2 sin²12° = cos24°.  Thus the numerator equals:   cos24° · cos24° = cos²24°. Denominator: 1. Note that sin²(–5°) = sin²5° because sine squared is even. 2. For sin(85°): 85° = 90° – 5° so sin85° = cos5°, and sin²85° = cos²5°. 3. Then, the denominator is:   sin²5° + cos²5° – sin²24° = 1 – sin²24°,  since sin²5° + cos²5° = 1. 4. But 1 – sin²24° = cos²24°. Thus, the entire fraction is:   cos²24° / cos²24° = 1. ───────────────────────────── Step (5): Evaluate   sin(140°) – cos(220°)·tan(–155°). 1. Write the angles in familiar forms:  • 140° = 180° – 40° ⟹ sin140° = sin40°.  • 220° = 180° + 40° ⟹ cos220° = –cos40°.  • tan(–155°) = –tan155° (since tan is odd).  • Also, 155° = 180° – 25° ⟹ tan155° = –tan25°, so   tan(–155°) = –(–tan25°) = tan25°. 2. Substitute these results back:   sin(140°) – cos(220°)·tan(–155°) = sin40° – [–cos40°]·tan25° = sin40° + cos40°·tan25°. 3. Write tan25° as sin25°/cos25°:   This becomes sin40° + (cos40°·sin25°)/cos25°. 4. Combine over a common denominator:   = [sin40°·cos25° + cos40°·sin25°] / cos25°.  The numerator is recognizable as sin(40° + 25°) by the sine addition formula:   sin40°·cos25° + cos40°·sin25° = sin65°. 5. Also note cos25° = sin(90°–25°) = sin65°.  Thus the fraction is sin65° / sin65° = 1. ───────────────────────────── Step (6): Evaluate   [cos⁴(190°) – sin⁴(–10°)] ÷ [cos(55°)·cos(325°)]. 1. Simplify the numerator:  • 190° = 180° + 10° ⟹ cos190° = –cos10° so cos⁴190° = (–cos10°)⁴ = cos⁴10°.  • sin(–10°) = –sin10° so sin⁴(–10°) = (–sin10°)⁴ = sin⁴10°.  Thus, the numerator is cos⁴10° – sin⁴10°. 2. Factor the difference of two fourth powers as a difference of squares:   cos⁴10° – sin⁴10° = (cos²10°)² – (sin²10°)² = (cos²10° – sin²10°)(cos²10° + sin²10°).  Since cos²10° + sin²10° = 1, this simplifies to:   cos²10° – sin²10°.  But cos²10° – sin²10° = cos20° (by the double‐angle formula). 3. Now simplify the denominator:  • 325° = 360° – 35° ⟹ cos325° = cos35°.  So the denominator is cos55°·cos35°.  Using the product-to-sum formula:   cos55°·cos35° = [cos(55° + 35°) + cos(55° – 35°)]/2 = [cos90° + cos20°]/2 = [0 + cos20°]/2 = cos20°/2. 4. Thus the whole expression becomes:   cos20° ÷ (cos20°/2) = 2. ───────────────────────────── Final Answers:  (3) = (√3)/2  (4) = 1  (5) = 1  (6) = 2