6. Trigonometric Identities and More Equations

Match each expression in Column I with its equivalent expression in Column II.

(tan (π/3) - tan (π/4))/(1 + tan (π/3) tan (π/4))

Be sure that you've familiarized yourself with the first set of formulas presented in this section by working C1–C4 in the Concept and Vocabulary Check. In Exercises 1–8, use the appropriate formula to express each product as a sum or difference.

$\cos \frac{3x}{2}\sin \frac{x}{2}$

In Exercises 25–32, write each expression as the sine, cosine, or tangent of an angle. Then find the exact value of the expression.

29. sin(5𝝅/12) cos(𝝅/4) - cos(5𝝅/12) sin(𝝅/4)

In Exercises 35–38, find the exact value of the following under the given conditions:

c. tan(α + β)

sin α = 3/5, 0 < α < 𝝅/2, and sin β = 12/13, 𝝅/2 < β < 𝝅.

In Exercises 35–38, find the exact value of the following under the given conditions:

a. sin(α + β)

sin α = 3/5, 0 < α < 𝝅/2, and sin β = 12/13, 𝝅/2 < β < 𝝅.