Question

已知arcsin(x-1)=arccos(3/5),那么x=?

答案9/5

Answer 1

cosarccos(3/5)=3/5
sinarccos(3/5)=4/5
x-1=sinarcsin(x-1)=sinarccos(3/5)=4/5
x=9/5

追问

为什么？sinarccos(3/5)=4/5

追答

0<arccos(3/5)<π
sinarccos(3/5)=根号[1-cos²arccos(3/5)]=根号（1-9/25)=4/5
注意把arccos(3/5)看成一个角