x属于〔π/4,5π/4）求arcsin (sinx+cosx/√2)的值
问题描述：
x属于〔π/4,5π/4）求arcsin (sinx+cosx/√2)的值
答
arcsin [(sinx+cosx)/√2]
=arcsin [√2sin(x+π/4)/√2]
=arcsin [sin(x+π/4)]
=arcsin[-sin(x+π/4-π)]
=-arcsin[sin(x-3π/4)]
=-(x-3π/4)
=3π/4-x