设X1,X2是方程x2-xsin(π/5)+cos(π/5)=0的两根,则arctanx1+arctanx2的值是?
人气:430 ℃ 时间:2020-06-15 01:28:42
解答
两根之和是x1+x2=sin(π/5),x1x2=cos(π/5)
tan[arctanx1+arctanx2]=(x1+x2)/(1-x1x2)=sin(π/5)/[1-cos(π/5)]我做到了,然后呢?tan[arctanx1+arctanx2]=(x1+x2)/(1-x1x2)=sin(π/5)/[1-cos(π/5)] =2sin(π/10)cos(π/10)/[2sin^2(π/10)]=cot(π/10)arctanx1+arctanx2=arccot(π/10)还是不对,这是道证明题,答案是2派/5这个实在做不出来,不知道你这题目错,不能化简了,你那个是用倍角公式,这个题目里没有用倍角公式的地方啊我实际上做的和你一样,谢谢
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