find sin2x, cos2x, and tan2x if tanx=1/2 in quadrant 1

Answer 1

sin2x=2tanx/(1+tan^2x)

          =2(1/2)/(1+(1/2)^2)

         =1/(1+(1/4))

         =1/(5/4)

         =4/5

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cos2x =(1-tan^2x)/(1+tan^2x)

            = (1-(1/2)^2)/(1+(1/2)^2)

            =(1-(1/4))/(1+(1/4))

             =(3/4)/(5/4)

             = 3/5

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tan 2x = sin 2x/cos2x =(4/5)/(3/5) =4/3