Question

FIND A QUADRATIC APPROXIMATION TO TAN θ , FOR θ ≈0. (Unit 3 2A.6)

I don't understand how θ/(1-(1/2)(θ^2)=θ. It's probably some identity I'm not using.

Answer 1

This isn't an equality, it's a quadratic approximation.
\[\theta \div ( 1 - \theta^2 /2)\] is about \[\theta * (1 + \theta^2/2)\] because you can multiply top and bottom by \[1 + \theta^2/2\] and then drop the 4th power in the denominator. This leaves a 1st and 3rd power, and when you drop the third power you are left with just theta.