若cos2a/sin(a-π/4)=-根号2/2 则sina+cosa 的值为多少?用高中知识回答
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若cos2a/sin(a-π/4)=-根号2/2 则sina+cosa 的值为多少?用高中知识回答
若cos2a/sin(a-π/4)=-根号2/2 则sina+cosa 的值为多少?用高中知识回答
若cos2a/sin(a-π/4)=-根号2/2 则sina+cosa 的值为多少?用高中知识回答
cos2a/sin(a-π/4)
=(cos²a-sin²a)/[(√2/2)(sina-cosa)]
=(cosa+sina)(cosa-sina)/[(√2/2)(sina-cosa)]
=-(cosa+sina)/(√2/2)
=-√2/2
所以
cosa+sina=1/2
(cos²a-sin²a)/(sinacosπ/4-cosasinπ/4)=-√2/2
(cos²a-sin²a)/[√2/2(sina-cosa)]=-√2/2
分子是平方差
所以原式=-1/2
cos2a/sin(a-π/4)
=(cos^2a-sin^2a)/[√2/2(sina-cosa)]
=√2(cosa+sina)(cosa-sina)/(sina-cosa)
=-√2(cosa+sina)
=-√2/2
sina+cosa=1/2
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