三角函数 (20 17:30:8)
若[cos2a] / sin(a-π/4)=-(根号2)/2 则 sina+cosa的值
人气:455 ℃ 时间:2020-02-03 18:08:34
解答
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
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