91Ó°ÊÓ

In Exercises \(99-107\), express the domain of the function using the extended interval notation. (See page 756 in Section 10.3 .1 for details.) $$ f(x)=\frac{\cos (x)}{\sin (x)+1} $$

In Exercises \(82-128\), verify the identity. Assume that all quantities are defined. $$ \sin ^{5}(\theta)=\left(1-\cos ^{2}(\theta)\right)^{2} \sin (\theta) $$

In Exercises \(82-128\), verify the identity. Assume that all quantities are defined. $$ \sec ^{10}(\theta)=\left(1+\tan ^{2}(\theta)\right)^{4} \sec ^{2}(\theta) $$

Find the exact value or state that it is undefined. $$ \arctan \left(\tan \left(\frac{2 \pi}{3}\right)\right) $$

Find the exact value or state that it is undefined. $$ \operatorname{arccot}\left(\cot \left(\frac{\pi}{3}\right)\right) $$

In Exercises \(99-107\), express the domain of the function using the extended interval notation. (See page 756 in Section 10.3 .1 for details.) $$ f(x)=\sqrt{2-\sec (x)} $$

In Exercises \(82-128\), verify the identity. Assume that all quantities are defined. $$ \cos ^{2}(\theta) \tan ^{3}(\theta)=\tan (\theta)-\sin (\theta) \cos (\theta) $$

In Exercises \(82-128\), verify the identity. Assume that all quantities are defined. $$ \sec ^{4}(\theta)-\sec ^{2}(\theta)=\tan ^{2}(\theta)+\tan ^{4}(\theta) $$

Find the exact value or state that it is undefined. $$ \operatorname{arccot}\left(\cot \left(-\frac{\pi}{4}\right)\right) $$

Find the exact value or state that it is undefined. $$ \operatorname{arccot}(\cot (\pi)) $$