2 sqrt 3-4 sqrt 3*sin^2 23pi/12

Question

2 sqrt 3-4 sqrt 3*sin^2 23pi/12

Answer 1

2√3 - 4√3 · sin²(23π/12) = 2√3 - 4√3 · sin²(2π - π/12) = 2√3 - 2√3 · 2sin²(-π/12) = 2√3 - 2√3 · (1 - cosπ/6) = 2√3 - 2√3 · (1 - √3/2) = 2√3 - 2√3 + 3 = 3