求sin^2π/5+sin^23π/5的值
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求sin^2π/5+sin^23π/5的值
sin方
sin方
![求sin^2π/5+sin^23π/5的值](/uploads/image/z/20056492-28-2.jpg?t=%E6%B1%82sin%5E2%CF%80%2F5%2Bsin%5E23%CF%80%2F5%E7%9A%84%E5%80%BC)
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
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
sin(2π+a) ,sin(π+a),sin(5π+a) 的区别
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