The curve is smooth and there is only one line that is (locally) entirely on one side of the curve.
there are two lines AB and CD which one is tangent line and why?
I know they say AB is tangent line but how to Mathematically( Geometrically(Trigonometrically )) prove it?
we can take tangent theta too and tangent psi too then both are through tangent of some angle so aren't they both tangent lines?
Ah well, let's see what wiki says:
As you can see, CD does not "just touch".Originally Posted by wiki
And if we look at the derivative, we'd be looking at a line through P and a second point on the curve.
When we let the second point approach P, we get the tangent line.
This is AB and not CD.
You need to review the definition of "tangent line". It has nothing to do with "tangent of an angle".we can take tangent theta too and tangent psi too then both are through tangent of some angle so aren't they both tangent lines?