6. Trigonometric Identities and More Equations

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

cos x/sec x + sin x/csc x

For each expression in Column I, use an identity to choose an expression from Column II with the same value. Choices may be used once, more than once, or not at all.

sin 35°

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

(tan x + cot x)²

For each expression in Column I, use an identity to choose an expression from Column II with the same value. Choices may be used once, more than once, or not at all.

-sin 35°

For each expression in Column I, choose the expression from Column II that completes an identity.

2. csc x = ____

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

(1 + tan θ)² - 2 tan θ

For each expression in Column I, use an identity to choose an expression from Column II with the same value. Choices may be used once, more than once, or not at all.

cos 75°

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

1/( sin α - 1) - 1/(sin α + 1)

For each expression in Column I, use an identity to choose an expression from Column II with the same value. Choices may be used once, more than once, or not at all.

sin 300°

Factor each trigonometric expression.

sec² θ - 1

For each expression in Column I, use an identity to choose an expression from Column II with the same value. Choices may be used once, more than once, or not at all.

cos(-55°)

Factor each trigonometric expression.

(tan x + cot x)² - (tan x - cot x)²

Factor each trigonometric expression.

4 tan² β + tan β - 3

Factor each trigonometric expression.

cot⁴ x + 3 cot² x + 2

Factor each trigonometric expression.

sin³ α + cos³ α