SOLUTION: use the sum and difference formulas to solve the equation on [0,2pi): cos(x+5pi/6)-cos(x-5pi/6)=1

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Question 614375: use the sum and difference formulas to solve the equation on [0,2pi): cos(x+5pi/6)-cos(x-5pi/6)=1
Answer by lwsshak3(11628) About Me  (Show Source):
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use the sum and difference formulas to solve the equation on [0,2pi):
cos(x+5pi/6)-cos(x-5pi/6)=1
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cos(x+5pi/6)-(cos(x-5pi/6)=1
cosxcos5π/6-sinxsin5π/6-(cosxcos5π/6+sinxsin5π/6)=1
cosxcos5π/6-sinxsin5π/6-cosxcos5π/6-sinxsin5π/6)=1
-2sinxsin5π/6=1
sin(5π/6)=1/2 in quadrant II
sinx=1/-2sin5π/6=1/(-2*(1/2))=1/-1=-1
x=3π/2