当α+в=30°时,sin²α+cos²в+cosαsinв的值为
来源:学生作业帮助网 编辑:作业帮 时间:2024/07/01 06:55:14
![当α+в=30°时,sin²α+cos²в+cosαsinв的值为](/uploads/image/z/1786663-55-3.jpg?t=%E5%BD%93%CE%B1%EF%BC%8B%D0%B2%EF%BC%9D30%C2%B0%E6%97%B6%2Csin%26%23178%3B%CE%B1%EF%BC%8Bcos%26%23178%3B%D0%B2%EF%BC%8Bcos%CE%B1sin%D0%B2%E7%9A%84%E5%80%BC%E4%B8%BA)
当α+в=30°时,sin²α+cos²в+cosαsinв的值为
当α+в=30°时,sin²α+cos²в+cosαsinв的值为
当α+в=30°时,sin²α+cos²в+cosαsinв的值为
结果=5/4
α+в=30°
B=π/6-a
sin²α+cos²в+cosαsinв
=sin²a+cos²(π/6-a)+cosasin(π/6-a)
=sin²a+(√3/2*cosa+1/2*sina)²+cosa(1/2cosa-√3/2*sina)
=sin²a+3/4*cos²a+√3/2*sinacosa+1/4sin²a+1/2*cos²a-√3/2*sinacosa
=5/4sin²a+5/4cos²a
=5/4(sin²a+cos²a)
=5/4
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