MAC 1114 Trigonometry
Section 5.1: Proving Identities
1) Prove sec θ cot θ = csc θ
2) Prove sin x (sec x + csc x ) = tan x + 1
3) Prove (sin4 t – cos4 t)/sin2 t cos2 t = sec2 t – csc2 t
4) Prove 1 + sin θ = cos2 θ/(1 – sin θ) and verify with a graphing calculator.
5) Prove sec θ – csc θ = (sin θ – cos θ)/sin θ cos θ
6) Prove cos t /(1 + sin t) = (1 – sin t)/cos t
7) Prove sin2 t/(1 – cos t)2 = (1 + cos t)/(1 – cos t)
8) Show that tan2 θ + cot2 θ = 1 is not an identity by finding a counter example.
1