3
$\begingroup$

I have an equation $x = \csc(\theta) - \cot(\theta).$

As $\theta$ approaches zero, $x$ approaches zero. However, trying to solve the equation at zero yields an undefined result.

How do I rewrite the equation to be continuous at 0?

1 Answers 1

5

Hint: Write the cosecant and cotangent in terms of sine and cosine. You can then combine the two fractions to give an expression that goes to 0/0. Expanding in a Taylor series or L'Hopital's rule will then be your friend.

  • 1
    @Rahul Narain ah! thats it. So rewriting and canceling gives me $\tan(\theta/2)$!2011-01-18