Question 86725: please help me solve this equation sin 2x-cosx=0
Answer by longjonsilver(2297)   (Show Source):
You can put this solution on YOUR website! need to get rid of either the sin or cos... to make an equation in just one "variable". The obvious one is the sin 2x since there is a formula:
sin2x = 2sinx cosx
so, 2sinXcosX - cosX = 0
looking at this, we have a cosX in both terms so we can factorise.... solving any equation we are always looking to factorise:
cosX(2sinX-1) = 0
which means that either
cosX=0 or 2sinX-1 = 0
cosX=0 or 2sinX = 1
cosX=0 or sinX = 1/2
X=90 or X=30... in the first quadrant. There are other angles that give these answers too but you do not quote the range of angles acceptable.
hope this helps
Jon
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