6. Trigonometric Identities and More Equations

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

Each expression simplifies to a constant, a single function, or a power of a function. Use fundamental identities to simplify each expression.

cot α sin α

Each expression simplifies to a constant, a single function, or a power of a function. Use fundamental identities to simplify each expression.

cot t tan t

Each expression simplifies to a constant, a single function, or a power of a function. Use fundamental identities to simplify each expression.

(csc θ sec θ)/cot θ

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

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

4. cot x = ____

Each expression simplifies to a constant, a single function, or a power of a function. Use fundamental identities to simplify each expression.

csc² t - 1