化简(2cos(x/2)^2-sinx-1)/(根号2sin(π/4+X))
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化简(2cos(x/2)^2-sinx-1)/(根号2sin(π/4+X))
[2cos(x/2)^2-sinx-1]/[√2sin(π/4+X)]
=[cosx+1-sinx-1]/[√2sin(π/4+X)]
=[cosx-sinx]/[√2sin(π/4+X)]
=√2[√2/2cosx-√2/2sinx]/[√2sin(π/4+X)]
=√2[cosπ/4cosx-sinπ/4sinx]/[√2sin(π/4+X)]
=√2[cos(π/4+x)]/[√2sin(π/4+X)]
=cos(π/4+x)/sin(π/4+X)
=cot(π/4+x)
=[cosx+1-sinx-1]/[√2sin(π/4+X)]
=[cosx-sinx]/[√2sin(π/4+X)]
=√2[√2/2cosx-√2/2sinx]/[√2sin(π/4+X)]
=√2[cosπ/4cosx-sinπ/4sinx]/[√2sin(π/4+X)]
=√2[cos(π/4+x)]/[√2sin(π/4+X)]
=cos(π/4+x)/sin(π/4+X)
=cot(π/4+x)
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