Question 668379
Please help me solve this equation using the double angle idenities. If secx= sqrt (3), sinx<0, find tan(2x)?
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sinx<0 in quadrants III and IV
secx>0 in quadrants I and IV
so, x is in quadrant IV
secx=&#8730;3/1=hypotenuse/adjacent side (in quadrant IV where sec>0
opposite side=&#8730;(3-1)=-&#8730;2
tanx=opposite side/adjacent side=-&#8730;2/1=-&#8730;2
Identity: 
tan 2x=(2 tanx)/(1-tan^2x)
=-2&#8730;2/(1-2)
=2&#8730;2