91Ó°ÊÓ

Use the formula for the cosine of the difference of two angles to solve Exercises \(1-12\) Verify each identity. $$ \cos \left(x-\frac{5 \pi}{4}\right)=-\frac{\sqrt{2}}{2}(\cos x+\sin x) $$

Use the given information to find the exact value of each of the following: a. \(\sin 2 \theta\) b. \(\cos 2 \theta\) c. \(\tan 2 \theta\) \(\sin \theta=-\frac{9}{41}, \theta\) lies in quadrant III.

Verify each identity. \(\frac{\tan \theta \cot \theta}{\csc \theta}=\sin \theta\)

Use one or more of the six sum and difference identities to solve Exercises \(13-54\) Find the exact value of each expression. $$ \sin \left(45^{\circ}-30^{\circ}\right) $$

Find all solutions of each equation. $$ \tan x=1 $$

express each sum or difference as a product. If possible, find this product’s exact value. $$ \cos 4 x+\cos 2 x $$

Use one or more of the six sum and difference identities to solve Exercises \(13-54\) Find the exact value of each expression. $$ \sin \left(60^{\circ}-45^{\circ}\right) $$

Use the given information to find the exact value of each of the following: a. \(\sin 2 \theta\) b. \(\cos 2 \theta\) c. \(\tan 2 \theta\) \(\sin \theta=-\frac{2}{3}, \theta\) lies in quadrant III.

Verify each identity. \(\frac{\cos \theta \sec \theta}{\cot \theta}=\tan \theta\)

express each sum or difference as a product. If possible, find this product’s exact value. $$ \cos 9 x-\cos 7 x $$