91Ó°ÊÓ

In Exercises \(165-184\), rewrite the quantity as algebraic expressions of \(x\) and state the domain on which the equivalence is valid. $$ \cos \left(\arcsin \left(\frac{x}{2}\right)\right) $$

In Exercises \(165-184\), rewrite the quantity as algebraic expressions of \(x\) and state the domain on which the equivalence is valid. $$ \cos (\arctan (3 x)) $$

In Exercises \(165-184\), rewrite the quantity as algebraic expressions of \(x\) and state the domain on which the equivalence is valid. $$ \sin (2 \arcsin (7 x)) $$

In Exercises \(165-184\), rewrite the quantity as algebraic expressions of \(x\) and state the domain on which the equivalence is valid. $$ \sin \left(2 \arcsin \left(\frac{x \sqrt{3}}{3}\right)\right) $$

In Exercises \(165-184\), rewrite the quantity as algebraic expressions of \(x\) and state the domain on which the equivalence is valid. $$ \sec (\arctan (2 x)) \tan (\arctan (2 x)) $$

In Exercises \(165-184\), rewrite the quantity as algebraic expressions of \(x\) and state the domain on which the equivalence is valid. $$ \sin (\arcsin (x)+\arccos (x)) $$

In Exercises \(165-184\), rewrite the quantity as algebraic expressions of \(x\) and state the domain on which the equivalence is valid. $$ \cos (\arcsin (x)+\arctan (x)) $$

In Exercises \(165-184\), rewrite the quantity as algebraic expressions of \(x\) and state the domain on which the equivalence is valid. $$ \tan (2 \arcsin (x)) $$

In Exercises \(165-184\), rewrite the quantity as algebraic expressions of \(x\) and state the domain on which the equivalence is valid. $$ \sin \left(\frac{1}{2} \arctan (x)\right) $$

In Exercises \(165-184\), rewrite the quantity as algebraic expressions of \(x\) and state the domain on which the equivalence is valid. $$ \text { If } \sin (\theta)=\frac{x}{2} \text { for }-\frac{\pi}{2}<\theta<\frac{\pi}{2} \text { , find an expression for } \theta+\sin (2 \theta) \text { in terms of } x \text { . } $$