Key Trigonometric Identities

Which of the following is the Pythagorean identity? A) sin²θ + cos²θ = 2 B) sin²θ + cos²θ = 1 C) sin²θ - cos²θ = 1 D) sin²θ × cos²θ = 1

• D) sin²θ × cos²θ = 1

• C) sin²θ - cos²θ = 1

• B) sin²θ + cos²θ = 1

• A) sin²θ + cos²θ = 2

What is the value of 1 + tan²θ? A) sec²θ B) csc²θ C) cos²θ D) sin²θ

• sin²θ

• sec²θ

• cot²θ

• tanθ

Which identity represents the double angle formula for sin(2θ)? A) 2sin²θ B) cos²θ - sin²θ C) 2sinθcosθ D) sinθ + cosθ

• 2cos²θ - 1

• C) 2sinθcosθ

• sin²θ + cos²θ

• sin(θ + θ)

What is cos(2θ) expressed in terms of cosine only? A) 2cos²θ B) 2cos²θ - 1 C) 1 - cos²θ D) cos²θ + 1

• cos²θ - 2

• 2cos²θ + 1

• B) 2cos²θ - 1

• 1 + cos²θ

Which of the following equals cot²θ + 1? A) sec²θ B) tan²θ C) csc²θ D) sin²θ

• secθ

• C) csc²θ

• tanθ

• cot²θ

What is the reciprocal identity of sin(θ)? A) cos(θ) B) tan(θ) C) csc(θ) D) sec(θ)

• sin(2θ)

• csc(θ)

• sec(θ)

• cot(θ)

Which formula represents sin(A + B)? A) sinA·cosB - cosA·sinB B) sinA·cosB + cosA·sinB C) sinA·sinB + cosA·cosB D) cosA·cosB - sinA·sinB

• B) sinA·cosB + cosA·sinB

• D) cosA·sinB + sinA·cosB

• A) sinA·cosB - cosA·sinB

• C) sinA·sinB - cosA·cosB

What is the value of cos(A - B)? A) cosA·cosB - sinA·sinB B) sinA·cosB - cosA·sinB C) cosA·cosB + sinA·sinB D) sinA·sinB - cosA·cosB

• C) cosA·cosB + sinA·sinB

• cosA·sinB + sinA·cosB

• sinA·cosB + cosA·sinB

• cosA·cosB - sinA·sinB

Which of the following is the half-angle identity for sin²θ? A) (1 + cos2θ)/2 B) (1 - cos2θ)/2 C) (1 - sin2θ)/2 D) (1 + sin2θ)/2

• (1 + sin2θ)/2

• (1 + cos2θ)/2

• (1 - tan2θ)/2

• (1 - cos2θ)/2

What is tan(2θ) equal to? A) 2tanθ/(1 - tan²θ) B) 2tanθ/(1 + tan²θ) C) tanθ/(1 - tan²θ) D) 2tan²θ/(1 - tanθ)

• tanθ/(1 + tan²θ)

• 2tanθ/(1 - tanθ)

• tan²θ/(1 + tan²θ)

• A) 2tanθ/(1 - tan²θ)