Question

How do you prove the identities? 1) 1- cos²Θ ≡ sin²Θ 2) (1-sin²Θ) tanΘ≡ cosΘ sinΘ

Answer 1

Hello :
1) 1- cos²Θ ≡ sin²Θ
cos²Θ + sin²Θ = 1
  sin²Θ = 1- cos²Θ


2) (1-sin²Θ) tanΘ≡ cosΘ sinΘ
 by 1) :
1-sin²Θ =cos²Θ
cos²Θ × tanΘ = cos²Θ × (sinΘ)/(cosΘ) =cosΘ sinΘ