You can put this solution on YOUR website! prove csc(5pi/2 -x)=secx
csc(5π/2-x)=secx
start with left side:
csc(5π/2-x)=1/sin(5π/2-x)
using sin addition formula: sin(x-y)=sinxcosy-cosxsiny
sin(5π/2-x)=(sin(5π/2)*cosx-cos(5π/2)*sin(x)
=(1*cosx-0*sinx)=cosx
csc(5π/2-x)=1/sin(5π/2-x)=1/cosx=secx
verified: left side=right side
note: 5π/2=reference angle of π/2
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