6. Trigonometric Identities and More Equations

Use the given information to find sin(x + y).

cos x = 2/9, sin y = - 1, x in quadrant IV, y in quadrant III

Verify that each equation is an identity. See Example 4.

tan(x - y) - tan(y - x) = 2(tan x - tan y)/(1 + tan x tan y)

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

cos(-15°)

Find the exact value of the expression.

$\(\sin\)15\(\degree\)$

Find the exact value of the expression.

$\(\cos\]\frac{5\pi}{12}\)$

Verify that each equation is an identity (Hint: cos 2x = cos(x + x).)

cos 2x = cos² x - sin² x

Verify that each equation is an identity.

sin(x + y)/cos(x - y) = (cot x + cot y)/(1 + cot x cot y)

Find the exact value of the expression.

$\(\cos\)80\(\degree\[\cos\)20\(\degree\)+\(\sin\)80\(\degree\]\sin\)20\(\degree\)$

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 ( 𝝅/3 + 𝝅/4 )

Use the given information to find tan(s + t). See Example 3.

cos s = -15/17 and sin t = 4/5, s in quadrant II and t in quadrant I

In Exercises 57–64, find the exact value of the following under the given conditions:

a. cos (α + β)

cos α = 8/17, α lies in quadrant IV, and sin β = -1/2, β lies in quadrant III.

Use identities to fill in each blank with the appropriate trigonometric function name.

tan 24° = 1/ _____ 66°