91Ó°ÊÓ

Assume that the range of arcsecant is \(\left[0, \frac{\pi}{2}\right) \cup\left(\frac{\pi}{2}, \pi\right]\) and that the range of arccosecant is \(\left[-\frac{\pi}{2}, 0\right) \cup\left(0, \frac{\pi}{2}\right]\) when finding the exact value. $$ \operatorname{arcsec}\left(\sec \left(\frac{\pi}{4}\right)\right) $$

In Exercises \(82-128\), verify the identity. Assume that all quantities are defined. $$ \frac{1}{\sec (\theta)-\tan (\theta)}=\sec (\theta)+\tan (\theta) $$

In Exercises \(82-128\), verify the identity. Assume that all quantities are defined. $$ \frac{1}{\csc (\theta)-\cot (\theta)}=\csc (\theta)+\cot (\theta) $$

In Exercises \(82-128\), verify the identity. Assume that all quantities are defined. $$ \frac{1}{\csc (\theta)+\cot (\theta)}=\csc (\theta)-\cot (\theta) $$

Assume that the range of arcsecant is \(\left[0, \frac{\pi}{2}\right) \cup\left(\frac{\pi}{2}, \pi\right]\) and that the range of arccosecant is \(\left[-\frac{\pi}{2}, 0\right) \cup\left(0, \frac{\pi}{2}\right]\) when finding the exact value. $$ \operatorname{arcsec}\left(\sec \left(\frac{5 \pi}{6}\right)\right) $$

In Exercises \(82-128\), verify the identity. Assume that all quantities are defined. $$ \frac{1}{1-\sin (\theta)}=\sec ^{2}(\theta)+\sec (\theta) \tan (\theta) $$

Assume that the range of arcsecant is \(\left[0, \frac{\pi}{2}\right) \cup\left(\frac{\pi}{2}, \pi\right]\) and that the range of arccosecant is \(\left[-\frac{\pi}{2}, 0\right) \cup\left(0, \frac{\pi}{2}\right]\) when finding the exact value. \(\operatorname{arcsec}\left(\sec \left(\frac{5 \pi}{3}\right)\right)\)

In Exercises \(82-128\), verify the identity. Assume that all quantities are defined. $$ \frac{1}{1+\sin (\theta)}=\sec ^{2}(\theta)-\sec (\theta) \tan (\theta) $$

In Exercises \(82-128\), verify the identity. Assume that all quantities are defined. $$ \frac{1}{1-\cos (\theta)}=\csc ^{2}(\theta)+\csc (\theta) \cot (\theta) $$

Assume that the range of arcsecant is \(\left[0, \frac{\pi}{2}\right) \cup\left(\frac{\pi}{2}, \pi\right]\) and that the range of arccosecant is \(\left[-\frac{\pi}{2}, 0\right) \cup\left(0, \frac{\pi}{2}\right]\) when finding the exact value. \(\operatorname{arccsc}\left(\csc \left(\frac{\pi}{6}\right)\right)\)