2020 · Q58
What is the value of sin²6° + sin²12° + sin²18° + … + sin²84° + sin²90°?
Elementary MathematicsTrigonometry
- A1
- B2
- C4
- D8
Explanation
Pair each term with its complement: sin²θ + sin²(90° − θ) = 1. The angles 6°, 12°, …, 84° form 7 such pairs summing to 7, and sin²90° = 1 adds 1 more: total 8. The seven complementary pairs contribute 7 and sin²90° contributes the final 1.