求sin^2π/5+sin^23π/5的值

题目

求sin^2π/5+sin^23π/5的值
sin方

答案

根据特殊角三角函数的值：
sin(π/5) = √(10-2√5)/4,sin(2π/5) = √(10+2√5)/4
sin^2(π/5) = [√(10-2√5)/4]^2 = (10-2√5)/16 = (5-√5)/8
sin^2(2π/5) = [√(10+2√5)/4]^2 = (10+2√5)/16 = (5+√5)/8
sin^2(π/5)+sin^2(3π/5)
= sin^2(π/5) + sin^2(π-2π/5)
= sin^2(π/5) + sin^2(2π/5)
= (5-√5)/8 + (5+√5)/8
= 5/4