Let K be a monotone increasing interval of Z, y = sin (π / 4 + X / 2) sin (π / 4-x / 2)

y=sin(π/4+x/2)sin(π/4-x/2)
=sin(π/4+x/2)sin[π/2-(π/4+x/2)]
=sin(π/4+x/2)cos(π/4+x/2)
=1/2sin(π/2+x)
=1/2cosx
The monotone increasing interval is
[2kπ-π,2kπ],k∈Z

Let K ∈ Z, the monotone increasing interval of function y = sin (π / 4 + X / 2) sin (π / 4-x / 2) be

y=sin(π/4+x/2)sin(π/4-x/2)
=-1/2(cosπ/2-cosx)
=1/2(cosx)
The increasing interval is x ∈ [2K π + π, 2 (K + 1) π] K ∈ Z

Solving the equation 5x + 2A = 3x + 2B about X

5x+2a=3x+2b
2x=2b-2a
x=b-a

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