若1-cosθ/4+sin^2θ=1/2,则(4+cos^3θ)(3+sin^3θ)=

Question

若1-cosθ/4+sin^2θ=1/2,则(4+cos^3θ)(3+sin^3θ)=

Answer 1

答
(1-cosθ)/(4+sin^2θ)=1/2
∴2-2cosθ=4+sin²θ
∴2-2cosθ=5-cos²θ
即cos²θ-2cosθ-3=0
解得
cosθ=-1或cosθ=3>1（舍去）
则sinθ=0
(4+cos³θ)(3+sin³θ)
=(4-1)(3+0)
=3×3
=9