91Ó°ÊÓ

\(17-34\) . An equation is given. (a) Find all solutions of the equation. (b) Find the solutions in the interval \([0,2 \pi) .\) $$ \tan 3 \theta+1=\sec 3 \theta $$

\(29-34\) Simplify the expression by using a Double-Angle Formula or a Half- Angle Formula. $$ \begin{array}{ll}{\text { (a) } \frac{2 \tan 7^{\circ}}{1-\tan ^{2} 7^{\circ}}} & {\text { (b) } \frac{2 \tan 7 \theta}{1-\tan ^{2} 7 \theta}}\end{array} $$

Verify the identity. $$ \frac{\tan x}{\sec x}=\sin x $$

\(17-34\) . An equation is given. (a) Find all solutions of the equation. (b) Find the solutions in the interval \([0,2 \pi) .\) $$ 3 \tan ^{3} \theta-3 \tan ^{2} \theta-\tan \theta+1=0 $$

Prove the identity. $$ \cos \left(x+\frac{\pi}{6}\right)+\sin \left(x-\frac{\pi}{3}\right)=0 $$

\(29-34\) Simplify the expression by using a Double-Angle Formula or a Half- Angle Formula. $$ \text { (a) } \cos ^{2} 34^{\circ}-\sin ^{2} 34^{\circ} \quad \text { (b) } \cos ^{2} 5 \theta-\sin ^{2} 5 \theta $$

\(25-38\) . Find all solutions of the given equation. $$ 3 \tan ^{2} \theta-1=0 $$

Verify the identity. $$ \frac{\cos u \sec u}{\tan u}=\cot u $$

\(29-34\) Simplify the expression by using a Double-Angle Formula or a Half- Angle Formula. $$ \begin{array}{ll}{\text { (a) } \cos ^{2} \frac{\theta}{2}-\sin ^{2} \frac{\theta}{2}} & {\text { (b) } 2 \sin \frac{\theta}{2} \cos \frac{\theta}{2}}\end{array} $$

Prove the identity. $$ \tan \left(x-\frac{\pi}{4}\right)=\frac{\tan x-1}{\tan x+1} $$