91Ó°ÊÓ

In Exercises \(57-86\), find the exact value or state that it is undefined. $$ \tan \left(\arctan \left(\frac{5}{12}\right)\right) $$

In Exercises \(59-73\), verify the identity. Assume all quantities are defined. $$ \cos (8 \theta)=128 \cos ^{8}(\theta)-256 \cos ^{6}(\theta)+160 \cos ^{4}(\theta)-32 \cos ^{2}(\theta)+1 \text { (HINT: Use the result to } $$

In Exercises \(57-86\), find the exact value or state that it is undefined. $$ \tan (\arctan (0.965)) $$

Solve the inequality. Express the exact answer in interval notation, restricting your attention to \(0 \leq x \leq 2 \pi\). $$ \tan (x) \geq \sqrt{3} $$

In Exercises \(57-86\), find the exact value or state that it is undefined. $$ \tan (\arctan (3 \pi)) $$

In Exercises \(59-73\), verify the identity. Assume all quantities are defined. $$ \sec (2 \theta)=\frac{\cos (\theta)}{\cos (\theta)+\sin (\theta)}+\frac{\sin (\theta)}{\cos (\theta)-\sin (\theta)} $$

Solve the inequality. Express the exact answer in interval notation, restricting your attention to \(0 \leq x \leq 2 \pi\). $$ \sec ^{2}(x) \leq 4 $$

Solve the inequality. Express the exact answer in interval notation, restricting your attention to \(0 \leq x \leq 2 \pi\). $$ \cos ^{2}(x)>\frac{1}{2} $$

In Exercises \(57-86\), find the exact value or state that it is undefined. $$ \cot (\operatorname{arccot}(1)) $$

In Exercises \(59-73\), verify the identity. Assume all quantities are defined. $$ \frac{1}{\cos (\theta)-\sin (\theta)}+\frac{1}{\cos (\theta)+\sin (\theta)}=\frac{2 \cos (\theta)}{\cos (2 \theta)} $$