Check the supposed identity by substituting a value for x. Let x=30°, then sin(2x)=√3/2, tan(x)=1/√3. The RHS becomes:
(2/√3)/(1+⅓)=(2/√3)/(4/3)=(2/√3)(3/4)=√3/2, so the identity appears to be true.
sin(2x)=2sin(x)cos(x)=
2(sin(x)/cos(x))cos2(x)=
2tan(x)/sec2(x)=
2tan(x)/(1+tan2(x)) QED
[sin2(x)+cos2(x)=1, so, dividing through by cos2(x):
tan2(x)+1=sec2(x)]