x属于〔π/4,5π/4)求arcsin (sinx+cosx/√2)的值

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x属于〔π/4,5π/4)求arcsin (sinx+cosx/√2)的值

x属于〔π/4,5π/4)求arcsin (sinx+cosx/√2)的值
x属于〔π/4,5π/4)求arcsin (sinx+cosx/√2)的值

x属于〔π/4,5π/4)求arcsin (sinx+cosx/√2)的值
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