Simplify: cos220∘+cos270∘sin220∘+sin270∘+cos(20∘+θ)−sin(70∘−θ)cos220∘+cos270∘sin220∘+sin270∘+cos(20∘+θ)−sin(70∘−θ)cos220∘+cos270∘sin220∘+sin270∘+cos(20∘+θ)−sin(70∘−θ)
Answer:
11
- cos220∘+cos270∘sin220∘+sin270∘+cos(20∘+θ)−sin(70∘−θ)=cos220∘+sin220∘sin220∘+cos220∘+cos(20∘+θ)−sin(90∘−(20∘+θ)){sin(90∘−θ)=cosθ and cos(90∘−θ)=sinθ=cos220∘+sin220∘sin220∘+cos220∘+cos(20∘+θ)−cos(20∘+θ)=1+0=1