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If `f(x)=(2x)/(1+x^2) ,` show that `f(tantheta)=sin2theta)`

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If `f(x)=(2x)/(1+x^2) ,` show that `f(tantheta)=sin2theta)`
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`f(tantheta)=(2tantheta)/((1+tan^(2)theta))=(2tantheta)/(sec^(2)theta)=(2sintheta)/(costheta)xxcos^(2)theta=2sintheta.costheta=sin20`
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