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That clears things up a bit. Thank you

Looks like the online graphing programs do not recognise the discontinuity for these kinds of graphs. I tried desmos, geogebra and wolfram alpha. They all converted the function to sin2x before graphing them. Is there a better graphing program out there that shows the discontinuity?

is f(x)= (2tan(x))/(1+tan^(2)(x)) a continuous function?