Question

若acosθ-sinθ=1,asinθ+cosθ=1,则sinθ=

答案分析，谢谢

Answer 1

(acosθ-sinθ)²=a²cos²θ+sin²θ-2asinθcosθ=1……①
(asinθ+cosθ)²=a²sin²θ+cos²θ-2asinθcosθ=1……②
①+②得：a²cos²θ+sin²θ+a²sin²θ+cos²θ=2
即a²(sin²θ+cos²θ)+(sin²θ+cos²θ)=2
a²+1=2
解得：a=±1
1°若a=1，
则cosθ-sinθ=1……③
sinθ+cosθ=1……④
④-③得：2sinθ=0
解得：sinθ=0
2°若a=-1
则-cosθ-sinθ=1……⑤
-sinθ+cosθ=1……⑥
⑤+⑥得：-2sinθ=2
解得：sinθ=-1

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Answer 2

(acosθ-sinθ)^2=1 (1)
(asinθ+cosθ)^2=1 (2)
(1)+(2)得到a^2=1.