Question

Find the principal value of sec^-1(-1)

Answer 1

We know that the principal value branch of cos^–1x & sec^–1x is [0, π].

Now, sec^–1(–1) = sec^–1(secπ)   (\(\because\) secπ \(=\frac{1}{\cos\pi}=\frac{1}{-1}=-1\))

= π

\(\therefore\) The principal value of sec^–1(–1) is π.