Question

Rewrite the following as an algebraic expression of x.
csc(arccos(x))

State the domain on which the equivalence is valid.

Answer 1

Using the pythagorean identity:

\[\csc(\cos^{-1} (x))=\frac{ 1 }{ \sin(\cos^{-1} (x)) }=\pm\frac{ 1 }{ \sqrt{1-\cos ^{2}(\cos^{-1}(x))} }=\pm \frac{ 1 }{ \sqrt{1-x^{2}} }\]

Domain: \[\forall x \in \mathbb{R} \]

Answer 2

thanks