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sin(2ArCsin1/3ArCCos1/5)

sin(2*arcsin(1/3)*arccos(1/5)) = 0.80208089008128

原式=sin(arcsin1/5)cos(arccos1/3)+ cos(arcsin1/5)sin(arccos1/3) =(1/5)*(1/3)+()下次再写,没时间要走啦

cos(arcsin1/2-arccos3/5)=cos(arcsin1/2)cos(arccos3/5)+sin(arcsin1/2)sin(arccos3/5)=根号3 /2*3/5+1/2*4/5=(3根号3+4)/10

设arcsin1/3=x,即sinx=1/3.sin2arcsin1/3=sin2x=2sinxcosx 由sinx2+cosx2=1解得cosx=正负3分之2倍根号2 所以sin2x=2sinxcosx=正负9分之4倍根号2

令a=arcsin(1/3), 则 a∈(0,π/2) b=arccos(-1/5) 则,b∈(π/2, π) sina=1/3, cosa=2√2/3, tana=√2/4 cosb=-1/5, sinb=2√6/5, tanb=-2√6 所以 tan(a+b)=(tana+tanb)/(1-tanatanb) 自己代入算,可以了吧

sin(arcsin1/2+arccos1/3)=sin(arcsin1/2)cos(arccos1/3)+cos(arcsin1/2)sin(arccos1/3)=1/2*1/3+根号(1-(1/2)^2)*根号(1-(1/3)^2)=1/6+(根号3)/2*2根号(2)/3=1/6+(根号6)/3=(1+2根号6)/6

sin(arcsin1/3+arccos1/3)显然arcsin1/3+arccos1/3=π/2所以,原式=sin(π/2)=1

原式=sin(arccos1/2)cos(arccos1/3)+cos(arccos1/2)sin(arccos1/3)=√3/2*1/3+1/2*2√2/3=(√3+2√2)/6

sin(arcsin1/5+arccos1/3)=sin(11.53696+70.53081) =sin82.06777 =0.376816

cos(2arccos1/3)=2(cosarccos1/3)^2 -1=2(1/3)^2-1=-7/9 这类题嘛,要是他要求不用计算机算的话,一般都有简单算法的,cosarccos1/3=1/3 这里是关键,arccos1/3表示余弦值为1/3的角度(arccos1/3代表的是角度)然后再求它(角度)的余弦值,很容易得出是1/3,像其他的三角函数一样推倒.

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