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The expression (sin70° + sin10°)/(cos70° + cos10°) equals:

Competition practiceTrigonometry
  • Atan30°
  • Bcot40°
  • Ctan40°
  • Dtan80°

Step-by-Step Solution

Sum to product: sin70° + sin10° = 2·sin40°·cos30° and cos70° + cos10° = 2·cos40°·cos30°. The common factor 2cos30° cancels, leaving sin40°/cos40° = tan40° ≈ 0.839. Check: 1.1133/1.3268 = 0.839.
Answer: C) tan40°

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