Question

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

Answer 1

According to given expression:

`y=\sec (\cot ^(-1)(-(3)/(4)))`

First solve the inner bracket:

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

Now put this value in above given expression:

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

So the value of given expression is 1.6640.