Simplifying Products of Binomials Involving Trigonometric Functions (7.2.3)

Question 1

• Four basic trigonometric identities:
  
  • tan θ = (sin θ)/cos θ
  • cos^2 θ + sin^2 θ = 1 (the Pythagorean identity)
  • 1 + tan^2 θ = sec^2 θ
  • 1 + cot^2 θ = csc^2 θ

Answer 1

• Four basic trigonometric identities:
  
  • tan θ = (sin θ)/cos θ
  • cos^2 θ + sin^2 θ = 1 (the Pythagorean identity)
  • 1 + tan^2 θ = sec^2 θ
  • 1 + cot^2 θ = csc^2 θ

Question 2

• To simplify a product of trigonometric expressions, first multiply everything out. Then use trig identities to simplify the result.

Answer 2

• To simplify a product of trigonometric expressions, first multiply everything out. Then use trig identities to simplify the result.

Question 3

• Review: Rewriting expressions in terms of sines and cosines often makes simplifying easier.

Answer 3

• Review: Rewriting expressions in terms of sines and cosines often makes simplifying easier.