Question

已知sin(x+π)=4/5,且sinxcosx<0,求2sin(x-π)+tan(π-x)/4cos(x-3π)的值

Answer 1

sin(x+π)=4/5
sin(x+π)=4/5
sinx=-4/5
∵sinxcosx<0
∴cosx>0
cosx=3/5
tanx=-4/3
2sin(x-π)+tan(π-x)/4cos(x-3π)
=-2sinx+tan(-x)/4cos(x-π)
=-2sinx+tanx/4cosx
=8/5+(-4/3)/(4*3/5)
=8/5-5/9
=47/45
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