Question

利用5倍角公式sin 5a =16(sina)^5-20(sina)^3+5sinacos 5a =16(cosa)^5

Answer 1

cos5 (π/10)=16[cos(π/10)]^5-20[cos(π/10)]^3+5cos(π/10)=0,

16[cos(π/10)]^4-20[cos(π/10)]^2+5=0,

[cos(π/10)]^2=(5+√5)/8,因为[cos(π/10)]^2＞3/4,所以[cos(π/10)]^2=(5-√5)/8应该舍去.

[sin(π/10)]^2=(6-2√5)/16,sin (π/10) 的值为(√5-1)/4.