三角函数 (20 17:30:8)若[cos2a] / sin(a-π/4)=-(根号2)/2 则 sina+cosa的值
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![三角函数 (20 17:30:8)若[cos2a] / sin(a-π/4)=-(根号2)/2 则 sina+cosa的值](/uploads/image/z/227037-21-7.jpg?t=%E4%B8%89%E8%A7%92%E5%87%BD%E6%95%B0+%2820+17%3A30%3A8%29%E8%8B%A5%5Bcos2a%5D+%2F+sin%28a-%CF%80%2F4%29%3D-%EF%BC%88%E6%A0%B9%E5%8F%B72%EF%BC%89%2F2+%E5%88%99+sina%2Bcosa%E7%9A%84%E5%80%BC)
三角函数 (20 17:30:8)若[cos2a] / sin(a-π/4)=-(根号2)/2 则 sina+cosa的值
三角函数 (20 17:30:8)
若[cos2a] / sin(a-π/4)=-(根号2)/2 则 sina+cosa的值
三角函数 (20 17:30:8)若[cos2a] / sin(a-π/4)=-(根号2)/2 则 sina+cosa的值
化简:
cos2a/sin(a-π/4)
=(2cos2a*cos(a-π/4)) /(2sin(a-π/4) cos(a-π/4))
=(2cos2a*cos(a-π/4)) /sin(2a-π/2)
=-(2cos2a*cos(a-π/4)) /cos2a
=-2*cos(a-π/4) =-√2/2
∴cos(a-π/4) =√2/4
即:
cosa*cos(π/4)+sina*sin(π/4)=√2/4
sina+cosa=1/2
由题意:cos2a=cos^2a-sin^2a=(cosa+sina)(cosa-sina)
所以[cos2a] / sin(a-π/4)
=(cosa+sina)(cosa-sina)/(sina*根号2/2 -cosa*根号2/2) =-(根号2)/2
即(cosa+sina)(cosa-sina)/(sina-cosa)=-1/2
即-(cosa+sina)=-1/2,故sina+cosa=1/2
[cos2a] / sin(a-π/4)=-√2/2
[cos2a] / sin(a-π/4)
=(cosa-sina)(cosa+sina)/[√2(sina-cosa)/2]
=-(cosa+sina)/(√2/2)
=-√2/2
所以sina+cosa=1/2