6. Trigonometric Identities and More Equations

Which of the following is not a variation of a Pythagorean identity?

Be sure that you've familiarized yourself with the second set of formulas presented in this section by working C5–C8 in the Concept and Vocabulary Check. In Exercises 9–22, express each sum or difference as a product. If possible, find this product's exact value. cos 3x/2 + cos 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.

cos 75°

Use the given information to find each of the following.

sin x/2 , given cos x = - 5/8, with π/2 < x < π

Find the remaining five trigonometric functions of θ.

csc θ = -5/2, θ in quadrant III

Use the given information to find each of the following.

cos x/2 , given cot x = -3, with π/2 < x < π

Simplify each expression.

±√[(1 - cos 5A)/(1 + cos 5A)]

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

1 - 1/sec² x

Verify that each equation is an identity.

sin² α + tan² α + cos² α = sec² α

Verify that each equation is an identity.

(1 + sin x + cos x)² = 2(1 + sin x) (1 + cos x)

Use a half-angle identity to find each exact value.

sin 165°

Find sinθ.

sec θ = 7/2, tan θ < 0

Verify that each equation is an identity.

sin θ + cos θ = sin θ/(1 - cot θ) + cos θ/(1 - tan θ)

In Exercises 39–46, use a half-angle formula to find the exact value of each expression. tan(7𝝅/8)

Use a half-angle identity to find each exact value.

cos 195°