Question

Evaluatesec(cot^-1(-3/4))

Answer 1

According to given expression:

$y=\sec (\cot ^{-1}(-\frac{3}{4}))$

First solve the inner bracket:

$\begin{gathered} x=\cot ^{-1}(-\frac{3}{4}) \\ \cot (x)=-\frac{3}{4} \\ \tan (x)=-\frac{4}{3} \\ x=\tan ^{-1}(-\frac{4}{3}) \\ x=-53.06 \end{gathered}$

Now put this value in above given expression:

$\begin{gathered} y=\sec (-53.06) \\ y=\frac{1}{\cos (-53.06}) \\ y=\frac{1}{0.6009} \\ y=1.6640 \end{gathered}$

So the value of given expression is 1.6640.