Use the identities for the cosine of a sum or difference to write each expression as a trigonometric function of θ alone.

cos(90° + θ)

Use the identities for the cosine of a sum or difference to write each expression as a trigonometric function of θ alone.

cos(270° + θ)

Find cos(s + t) and cos(s - t).

cos s = - 8/17 and cos t = - 3/5, s and t in quadrant III​​

Find cos(s + t) and cos(s - t).

sin s = 2/3 and sin t = -1/3, s in quadrant II and t in quadrant IV​​

Find cos(s + t) and cos(s - t).

cos s = √2/4 and sin t = - √5/6, s and t in quadrant IV

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

cos( π/2 + x) = -sin x

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 (Hint: cos 2x = cos(x + x).)

cos 2x = 1 - 2 sin² x

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

cos 2x = (cot² x - 1)/(cot² x + 1)

Write each function as an expression involving functions of θ or x alone. See Example 2.

sin (3π/4 - x)

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

sin 60° cos 45° - cos 60° sin 45°

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))

Find the exact value of each expression.

sin 255°

Find the exact value of each expression.

tan 285°

Find the exact value of each expression.

sin (13π/12)

Find the exact value of each expression.

tan (5π/12)

Find the exact value of each expression.

sin (π/12)

Find the exact value of each expression.

sin (- 5π/12)

Find the exact value of each expression.

tan (-7π/12)

Find the exact value of each expression.

sin (-13π/12)

Find the exact value of each expression. See Example 1.

sin 40° cos 50° + cos 40° sin 50°

Find the exact value of each expression. See Example 1.

sin 5π/9 cos π/18 - cos 5π/9 sin π/18 .

Find the exact value of each expression. See Example 1.

[tan 80° - tan(-55°)]/[ 1 + tan 80° tan(-55°)]

Find the exact value of each expression. See Example 1.

[tan 5π/12 + tan π/4]/[1 - tan 5π/12 tan π/4]

Write each function as an expression involving functions of θ or x alone. See Example 2.

cos(θ - 30°)

Write each function as an expression involving functions of θ or x alone. See Example 2.

cos(45° - θ)

Write each function as an expression involving functions of θ or x alone. See Example 2.

sin(45° + θ)

Write each function as an expression involving functions of θ or x alone. See Example 2.

tan (π/4 + x)

Write each function as an expression involving functions of θ or x alone. See Example 2.

tan(180° + θ)

Write each function as an expression involving functions of θ or x alone. See Example 2.

sin(π + x)