6. Trigonometric Identities and More Equations

Find $\(\cos\]\left\)(a+b\(\right\))$ given $\(\cos\) a=\(\frac\)12$, $\(\sin\) b=\(\frac\)12$, & $a$ is in Q IV and $b$ is in Q II.

Use one or more of the six sum and difference identities to solve Exercises 13–54. In Exercises 13–24, find the exact value of each expression. tan ( 5𝝅/3 ﹣ 𝝅/4)

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

c. tan(α + β)

sin α = -1/3, 𝝅 < α < 3𝝅/2, and cos β = -1/3, 𝝅 < β < 3𝝅/2

Write each function value in terms of the cofunction of a complementary angle.

sin 15°

Use a sum or difference formula to find the exact value of each expression. cos(45° + 30°)

Find one value of θ or x that satisfies each of the following.

sec x = csc (2π/3)

Find the exact value of each expression. (Do not use a calculator.)

cos (7π/9) cos (2π/9) - sin (7π/9) sin (2π/9)

In Exercises 69–74, rewrite each expression as a simplified expression containing one term. cos (α + β) cos β + sin (α + β) sin β

Write each function value in terms of the cofunction of a complementary angle.

sin 142° 14'

Find the exact value of each expression.

tan (-7π/12)