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

Question

asked May 20, 2023 5.5k views

1 Answer

Moon Cheesez · Answer 1 · 2023-05-24T13:41:58+0000

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.