第二问怎么做,,,
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f(x)=cos2xsin2x + (1/2)cos4x
=(1/2)sin4x + (1/2)cos4x
=(1/2)(sin4x + cos4x)
=(√2/2)sin(4x + π/4)
∵f(α)=(√2/2)sin(4α+π/4)=√2/2
∴sin(4α + π/4)=1
∴4α + π/4=2kπ + π/2
4α=2kπ + π/2 - π/4
4α=2kπ + π/4
α=kπ/2 + π/16,k∈Z
∵α∈(π/2,π)
∴α=9π/16
=(1/2)sin4x + (1/2)cos4x
=(1/2)(sin4x + cos4x)
=(√2/2)sin(4x + π/4)
∵f(α)=(√2/2)sin(4α+π/4)=√2/2
∴sin(4α + π/4)=1
∴4α + π/4=2kπ + π/2
4α=2kπ + π/2 - π/4
4α=2kπ + π/4
α=kπ/2 + π/16,k∈Z
∵α∈(π/2,π)
∴α=9π/16
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