满足arcsinx+arctan(1/7)=派/4的x值等于
人气:294 ℃ 时间:2020-05-29 08:37:57
解答
设arctan(1/7)=a,则arcsinx=派/4-a
有:tana=1/7,sin(派/4-a)=(根号2)/2*(cosa-sina)=x
根据 arc函数定义,a为锐角,
tana=sina/cosa=[根号(1-cosa的平方)]/cosa=1/7
cosa=(-1+根号9605)/98,则sina=根号(2根号9605-2)/98
x=(根号2)/2*{(-1+根号9605)/98-根号(2根号9605-2)/98}
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