91Ó°ÊÓ

Solving a Trigonometric Equation In Exercises \(25-38,\) find all solutions of the equation in the interval \(0,2 \pi ) .\) $$\sec x+\tan x=1$$

Using Half-Angle Formulas, (a) determine the quadrant in which \(u\) 2 lies, and (b) find the exact values of \(\sin (u\) 2), \(\cos (u\) 2), and \(\tan (u\) 2) using the half-angle formulas. $$\tan u=-5 / 12, \quad 3 \pi / 2

Solving a Multiple-Angle Equation In Exercises \(39-44,\) solve the multiple-angle equation. $$2 \cos 2 x-1=0$$

Verify the identity. $$\frac{\tan x+\cot y}{\tan x \cot y}=\tan y+\cot x$$

Evaluating a Trigonometric Expression In Exercises \(35-40\) , find the exact value of the expression. $$ \frac{\tan (5 \pi / 6)-\tan (\pi / 6)}{1+\tan (5 \pi / 6) \tan (\pi / 6)} $$

Use the fundamental identities to simplify the expression. There is more than one correct form of each answer. \(\frac{1-\sin ^{2} x}{\csc ^{2} x-1}\)

Use the fundamental identities to simplify the expression. There is more than one correct form of each answer. \(\frac{\tan \theta \cot \theta}{\sec \theta}\)

Using Half-Angle Formulas, (a) determine the quadrant in which \(u\) 2 lies, and (b) 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

Solving a Multiple-Angle Equation In Exercises \(39-44,\) solve the multiple-angle equation. $$2 \sin 2 x+\sqrt{3}=0$$

Evaluating a Trigonometric Expression In Exercises \(35-40\) , find the exact value of the expression. $$ \frac{\tan 25^{\circ}+\tan 110^{\circ}}{1-\tan 25^{\circ} \tan 110^{\circ}} $$