Question

已知1+sinθ根号下(1-cos^2θ)+cosθ根号下(1-sin^2θ)=0,则θ的取值范围是?

Answer 1

1+sinθ根号(1-cos^2θ)+cosθ根号下(1-sin^2θ)=0

1+sinθ根号(sin^2θ)+cosθ根号下(cos^2θ)=0

1 + sinθ |sinθ| + cosθ |cosθ| = -1

sinθ |sinθ| + cosθ |cosθ| = -1

∵ -1≤sinθ |sinθ|≤1,-1≤ cosθ |cosθ|≤1

又：sinθ |sinθ| + cosθ |cosθ| = -1

∴ -1≤sinθ |sinθ|≤0,-1≤cosθ |cosθ|≤0

∴2kπ+π≤θ≤2kπ+3π/2