Question

what is the most usable half angle formulas in calculus ? i searched the internet for them but they were very complex and never used any of them to solve calculus problems in limit and continuity

Answer 1

I always think of half angle formulae as the method of last resort...

\[\tan(\frac{\theta}{2}) = t\]

this comes from the triangle



and if you use the double angle formulae you can then get

\[\tan(\theta) = \frac{2t}{1 -t^2}\]

\[\sin (\theta) = \frac{2t}{1 + t^2}\]

\[\cos(\theta) = \frac{1 - t^2}{1 + t^2}\]

hope this makes some sense...