Write each expression in terms of sine and cosine, and then simplify the expression so that no quotients appear and all functions are of θ only. See Example 3.

(sin θ - cos θ) (csc θ + sec θ)

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

For each expression in Column I, choose the expression from Column II that completes an identity. One or both expressions may need to be rewritten.

-tan x cos x

II

A. sin ^2 x/cos ^2 x

B.1/(sec ^2 x)

C. sin (-x)

D. csc ^2 x-cot ^2 x + sin ^2 x

E. tan x

Write each expression in terms of sine and cosine, and then simplify the expression so that no quotients appear and all functions are of θ only. See Example 3.

[1 - sin²(-θ)]/[1 + cot²(-θ)]

Write each expression in terms of sine and cosine, and then simplify the expression so that no quotients appear and all functions are of θ only. See Example 3.

(sec²θ - 1)/(csc²θ - 1)

Perform each indicated operation and simplify the result so that there are no quotients.

sec x/csc x + csc x/sec x

Perform each indicated operation and simplify the result so that there are no quotients.

cos β(sec β + csc β)

Perform each indicated operation and simplify the result so that there are no quotients.

cos x/sec x + sin x/csc x

Perform each indicated operation and simplify the result so that there are no quotients.

(tan x + cot x)²

Verify that each equation is an identity.

sin³ θ + cos³ θ = (cos θ + sin θ) (1 - cos θ sin θ)

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

cos(-15°)

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

cos 105° (Hint: 105° = 60° + 45°)

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

cos π/12

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

cos (-7π/12)

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

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

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

sin 15°

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

sin (2π/5)

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

sin 142° 14'

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

cot (9π/10)

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

tan 174° 03'

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

sin 98.0142°

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

sin 2π/3 = _____ (- π/6)

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

____ 72° = cot 18°

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

tan 24° = 1/ _____ 66°

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

tan θ = cot(45° + 2θ)

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

sin θ = cos(2θ + 30°)

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

sec x = csc (2π/3)

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

cos x = sin (π/12)

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(θ - 270°)