91Ó°ÊÓ

In Exercises 51-54, write the trigonometric expression as an algebraic expression. $$ \sin (\arctan 2 x-\arccos x) $$

In Exercises \(45-54\), use a graphing utility to approximate the solutions (to three decimal places) of the equation in the interval \([0,2 \pi)\). $$ \csc ^{2} x+0.5 \cot x-5=0 $$

In Exercises 45-56, factor the expression and use the fundamental identities to simplify. There is more than one correct form of each answer. $$ 1-2 \cos ^{2} x+\cos ^{4} x $$

In Exercises 49-54, find the exact values of \(\sin (u / 2)\), \(\cos (u / 2)\), and \(\tan (u / 2)\) using the half-angle formulas. $$ \cot u=3, \quad \pi

In Exercises 49-54, find the exact values of \(\sin (u / 2)\), \(\cos (u / 2)\), and \(\tan (u / 2)\) using the half-angle formulas. $$ \csc u=-\frac{5}{3}, \quad \pi

In Exercises 51-54, write the trigonometric expression as an algebraic expression. $$ \cos (\arccos x+\arcsin x) $$

\(\cos ^{2} 20^{\circ}+\cos ^{2} 52^{\circ}+\cos ^{2} 38^{\circ}+\cos ^{2} 70^{\circ}\)

In Exercises \(45-54\), use a graphing utility to approximate the solutions (to three decimal places) of the equation in the interval \([0,2 \pi)\). $$ 2 \tan ^{2} x+7 \tan x-15=0 $$

In Exercises 45-56, factor the expression and use the fundamental identities to simplify. There is more than one correct form of each answer. $$ \sin ^{4} x-\cos ^{4} x $$

In Exercises 49-54, find the exact values of \(\sin (u / 2)\), \(\cos (u / 2)\), and \(\tan (u / 2)\) using the half-angle formulas. $$ \sec u=-\frac{7}{2}, \quad \frac{\pi}{2}