91Ó°ÊÓ

Use one or more of the six sum and difference identities to solve Exercises \(13-54\) Write each expression as the sine, cosine, or tangent of an angle. Then find the exact value of the expression. $$ \sin \frac{7 \pi}{12} \cos \frac{\pi}{12}-\cos \frac{7 \pi}{12} \sin \frac{\pi}{12} $$

Involve equations with multiple angles. Solve each equation on the interval \([0,2 \pi)\) $$ \tan \frac{x}{2}=\sqrt{3} $$

Use one or more of the six sum and difference identities to solve Exercises \(13-54\) Write each expression as the sine, cosine, or tangent of an angle. Then find the exact value of the expression. $$ \frac{\tan \frac{\pi}{5}-\tan \frac{\pi}{30}}{1+\tan \frac{\pi}{5} \tan \frac{\pi}{30}} $$

Verify each identity. \(\frac{\cos x}{1-\sin x}+\frac{1-\sin x}{\cos x}=2 \sec x\)

Verify each identity. $$ \sin 2 t-\tan t=\tan t \cos 2 t $$

Involve equations with multiple angles. Solve each equation on the interval \([0,2 \pi)\) $$ \tan \frac{x}{2}=\frac{\sqrt{3}}{3} $$

Use one or more of the six sum and difference identities to solve Exercises \(13-54\) Write each expression as the sine, cosine, or tangent of an angle. Then find the exact value of the expression. $$ \frac{\tan \frac{\pi}{5}+\tan \frac{4 \pi}{5}}{1-\tan \frac{\pi}{5} \tan \frac{4 \pi}{5}} $$

Verify each identity. $$ \sin 2 t-\cot t=-\cot t \cos 2 t $$

the graph with the given equation is shown in \(a\left[0,2 \pi, \frac{\pi}{2}\right] b y[-2,2,1]\) viewing rectangle. a. Describe the graph using another equation. b. Verify that the two equations are equivalent. $$ y=\frac{\cos x-\cos 3 x}{\sin x+\sin 3 x} $$

Verify each identity. \(\frac{\sin x}{\cos x+1}+\frac{\cos x-1}{\sin x}=0\)