6. Trigonometric Identities and More Equations

Simplify each expression.

± √[(1 + cos (x/4))/2]

Select the expression with the same value as the given expression.

$\(\sin\[\left\)(-38\(\degree\]\right\))$

Verify that each equation is an identity.

(csc θ + cot θ)/(tan θ + sin θ) = cot θ csc θ

Use the Pythagorean identities to rewrite the expression as a single term.

$\(\left\)(1+\(\csc\[\theta\]\right\))\(\left\)(1-\(\csc\[\theta\]\right\))$

Let csc x = -3. Find all possible values of (sin x + cos x)/sec x.

Be sure that you've familiarized yourself with the second set of formulas presented in this section by working C5–C8 in the Concept and Vocabulary Check. In Exercises 9–22, express each sum or difference as a product. If possible, find this product's exact value. sin 6x + sin 2x

Find sinθ.

cos (-θ) = (√3)/6, cot θ < 0

Factor each trigonometric expression.

4 tan² β + tan β - 3

Simplify each expression.

√[(1 + cos 165°)/(1 - cos 165°)]