Exer. 1730: Use the binomial theorem to expand and simplify.

Trigonometry Notes Chapter 2 Section 1&2 Pythagorean Identities: Sin θ+Cos θ=1 Tan θ+1=Sec θ 2 1+Cot θ=Csc θ 2 Conjugates: 2 2 A+B--------A-B so (a+b)*(a-b)=a -b Verify the Identity: sinθ 1+cosθ = Binomial in the denominator is not good 1−cosθ sinθ sinθ ∗(1+cosθ) 1−cosθ Multiply by conjugate (1+cosθ) sinθ(1+cosθ) 2 (1-cosθ)(1+cosθ)=sin2θ because 1-cosθ=sinθ sin θ 1+cosθ 1+cosθ = Factor out sinθ sinθ sinθ Replace with single term: Tan θ+1=Sec θ 2 Sec θ+1=N/