Simplify cos210∘+cos280∘sin210∘+sin280∘+sin(90∘−θ)sinθtanθ+cos(90∘−θ)cosθcotθ
Answer:
2
- cos210∘+cos280∘sin210∘+sin280∘+sin(90∘−θ)sinθtanθ+cos(90∘−θ)cosθcotθ=cos210∘+cos2(90∘−10∘)sin210∘+sin2(90∘−10∘)+cosθsinθtanθ+sinθcosθcotθ{sin(90∘−θ)=cosθ and cos(90∘−θ)=sinθ=cos210∘+sin10∘sin210∘+cos210∘+cosθsinθtanθ+sinθcosθcotθ=1+cos2θ+sin2θ=1+1=2