sina+cosa=1/5、sin²a+cos²a=1,=>sin²a+(1/5-sin²a)=1,=>sin²a+(1/5-sin²a)=1sin²a-(2/5)sina+(1/25)+sin²a=12sin²a-(2/5)sina-(24/25)=025sin²a-5sina-12=0(5sina+3)(5sina-4)=
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![sina+cosa=1/5、sin²a+cos²a=1,=>sin²a+(1/5-sin²a)=1,=>sin²a+(1/5-sin²a)=1sin²a-(2/5)sina+(1/25)+sin²a=12sin²a-(2/5)sina-(24/25)=025sin²a-5sina-12=0(5sina+3)(5sina-4)=](/uploads/image/z/4020044-68-4.jpg?t=sina%2Bcosa%3D1%2F5%E3%80%81sin%26%23178%3Ba%2Bcos%26%23178%3Ba%3D1%2C%EF%BC%9D%EF%BC%9Esin%26%23178%3Ba%2B%EF%BC%881%2F5-sin%26%23178%3Ba%EF%BC%89%3D1%2C%EF%BC%9D%EF%BC%9Esin%26%23178%3Ba%2B%EF%BC%881%2F5-sin%26%23178%3Ba%EF%BC%89%3D1sin%26%23178%3Ba%EF%BC%8D%282%2F5%29sina%EF%BC%8B%281%2F25%29%EF%BC%8Bsin%26%23178%3Ba%3D12sin%26%23178%3Ba%EF%BC%8D%282%2F5%29sina%EF%BC%8D%2824%2F25%29%3D025sin%26%23178%3Ba%EF%BC%8D5sina%EF%BC%8D12%3D0%285sina%EF%BC%8B3%29%285sina%EF%BC%8D4%29%3D)
sina+cosa=1/5、sin²a+cos²a=1,=>sin²a+(1/5-sin²a)=1,=>sin²a+(1/5-sin²a)=1sin²a-(2/5)sina+(1/25)+sin²a=12sin²a-(2/5)sina-(24/25)=025sin²a-5sina-12=0(5sina+3)(5sina-4)=
sina+cosa=1/5、sin²a+cos²a=1,=>sin²a+(1/5-sin²a)=1,
=>sin²a+(1/5-sin²a)=1
sin²a-(2/5)sina+(1/25)+sin²a=1
2sin²a-(2/5)sina-(24/25)=0
25sin²a-5sina-12=0
(5sina+3)(5sina-4)=0
sina=-3/5【舍去】,sina=4/5
问:2sin²a-(2/5)sina-(24/25)=0这步中的2/5是怎么得的?
sina+cosa=1/5、sin²a+cos²a=1,=>sin²a+(1/5-sin²a)=1,=>sin²a+(1/5-sin²a)=1sin²a-(2/5)sina+(1/25)+sin²a=12sin²a-(2/5)sina-(24/25)=025sin²a-5sina-12=0(5sina+3)(5sina-4)=
(a-b)²=a²-2ab+b²,则:
[sina-(1/5)]²=(sina)²-2×(1/5)×(sina)+(1/5)²=sin²a-(2/5)sina+(1/25)
则:
sin²a-(2/5)sina+(1/25)+sin²a=1
2sin²a-(2/5)sina-(24/25)=0
…………
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