2026 · Q49
If (cos 35° + cos 55°) = p, then what is sin 35° ⋅ cos 35° equal to?
Elementary MathematicsTrigonometry
- A(1 − p²)/2
- B(p² − 1)/2
- C(1 + p²)/2
- D(p − 1)/2
Explanation
Square p = cos 35° + cos 55° = cos 35° + sin 35°. Expanding gives p² = cos²35° + sin²35° + 2sin 35°cos 35° = 1 + 2sin 35°cos 35°. Rearranging yields sin 35°·cos 35° = (p² − 1)/2, option B.