计算cos(π/3+arcsin4/5)=?

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计算cos(π/3+arcsin4/5)=?
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计算cos(π/3+arcsin4/5)=?
计算cos(π/3+arcsin4/5)=?

计算cos(π/3+arcsin4/5)=?
由题意不妨令α=arcsin4/5,那么:
sinα=4/5且可知0<α<π/2
则有:cosα=根号(1-sin²α)=3/5
所以:
cos(π/3+arcsin4/5)
=cos(π/3+α)
=cos(π/3)cosα -sin(π/3)sinα
=(1/2)*(3/5) - (根号3)/2 *(4/5)
=(3- 4根号3)/10

11/10

展开算原式=cos(π/3)cos(arcsin4/5)-sin(π/3)sin(ascsin4/5)=(1/2)X(3/5)-(√3/2)X(4/5)=(3-4√3)/10