求值:cos(3π/8-θ)cos(5π/24-θ)+sin(π/8+θ)sin(7π/24+θ)学到三角恒等式的 诱导公式 那里求值:cos(3π/8-θ)cos(5π/24-θ)+sin(π/8+θ)sin(7π/24+θ)我算到一半算不下去了π是派(pai)哦...=2cos(3π/8-θ)cos(5π/24-θ) =
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![求值:cos(3π/8-θ)cos(5π/24-θ)+sin(π/8+θ)sin(7π/24+θ)学到三角恒等式的 诱导公式 那里求值:cos(3π/8-θ)cos(5π/24-θ)+sin(π/8+θ)sin(7π/24+θ)我算到一半算不下去了π是派(pai)哦...=2cos(3π/8-θ)cos(5π/24-θ) =](/uploads/image/z/10260335-47-5.jpg?t=%E6%B1%82%E5%80%BC%EF%BC%9Acos%283%CF%80%2F8-%CE%B8%29cos%285%CF%80%2F24-%CE%B8%29%2Bsin%28%CF%80%2F8%2B%CE%B8%29sin%287%CF%80%2F24%2B%CE%B8%29%E5%AD%A6%E5%88%B0%E4%B8%89%E8%A7%92%E6%81%92%E7%AD%89%E5%BC%8F%E7%9A%84+%E8%AF%B1%E5%AF%BC%E5%85%AC%E5%BC%8F+%E9%82%A3%E9%87%8C%E6%B1%82%E5%80%BC%EF%BC%9Acos%283%CF%80%2F8-%CE%B8%29cos%285%CF%80%2F24-%CE%B8%29%2Bsin%28%CF%80%2F8%2B%CE%B8%29sin%287%CF%80%2F24%2B%CE%B8%29%E6%88%91%E7%AE%97%E5%88%B0%E4%B8%80%E5%8D%8A%E7%AE%97%E4%B8%8D%E4%B8%8B%E5%8E%BB%E4%BA%86%CF%80%E6%98%AF%E6%B4%BE%28pai%29%E5%93%A6...%3D2cos%283%CF%80%2F8-%CE%B8%29cos%285%CF%80%2F24-%CE%B8%29+%3D)
求值:cos(3π/8-θ)cos(5π/24-θ)+sin(π/8+θ)sin(7π/24+θ)学到三角恒等式的 诱导公式 那里求值:cos(3π/8-θ)cos(5π/24-θ)+sin(π/8+θ)sin(7π/24+θ)我算到一半算不下去了π是派(pai)哦...=2cos(3π/8-θ)cos(5π/24-θ) =
求值:cos(3π/8-θ)cos(5π/24-θ)+sin(π/8+θ)sin(7π/24+θ)
学到三角恒等式的 诱导公式 那里
求值:cos(3π/8-θ)cos(5π/24-θ)+sin(π/8+θ)sin(7π/24+θ)
我算到一半算不下去了
π是派(pai)哦...
=2cos(3π/8-θ)cos(5π/24-θ)
=cos(3π/8-θ-5π/24+θ)+cos(3π/8-θ+5π/24-θ)
只是搞不懂这两步之间怎么变过去的...我自己就做到=2cos(3π/8-θ)cos(5π/24-θ) 这步
求值:cos(3π/8-θ)cos(5π/24-θ)+sin(π/8+θ)sin(7π/24+θ)学到三角恒等式的 诱导公式 那里求值:cos(3π/8-θ)cos(5π/24-θ)+sin(π/8+θ)sin(7π/24+θ)我算到一半算不下去了π是派(pai)哦...=2cos(3π/8-θ)cos(5π/24-θ) =
注意关系3π/8-θ=π/2-(π/8+θ)
5π/24-θ=π/2-(7π/24+θ)
所以原式=cos(3π/8-θ)cos(5π/24-θ)+cos(3π/8-θ)sin(7π/24+θ)
=cos(3π/8-θ)cos(5π/24-θ)+cos(3π/8-θ)cos(5π/24-θ)
=2cos(3π/8-θ)cos(5π/24-θ)
=cos(3π/8-θ-5π/24+θ)+cos(3π/8-θ+5π/24-θ)
=cosπ/6+cos(7/12π-2θ)
这是积化合差公式
cosA*cosB=1/2[cos(A-B)+cos(A+B)]
cos(3π/8-θ)cos(5π/24-θ)+sin(π/8+θ)sin(7π/24+θ)
=cos[π/2-(π/8+θ)]cos[π/2-(7π/24+θ)]+sin(π/8+θ)sin(7π/24+θ)
=sin(π/8+θ)sin(7π/24+θ)+sin(π/8+θ)sin(7π/24+θ)
=2sin(π/8+θ)sin(7π/24+θ)
=2*(-1...
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cos(3π/8-θ)cos(5π/24-θ)+sin(π/8+θ)sin(7π/24+θ)
=cos[π/2-(π/8+θ)]cos[π/2-(7π/24+θ)]+sin(π/8+θ)sin(7π/24+θ)
=sin(π/8+θ)sin(7π/24+θ)+sin(π/8+θ)sin(7π/24+θ)
=2sin(π/8+θ)sin(7π/24+θ)
=2*(-1/2)[cos(π/8+θ+7π/24+θ)-cos(π/8+θ-(7π/24+θ))
=-[cos(5π/12+2θ)-cos(-π/6)]
=cos(π/6)-cos(5π/12+2θ)
=√3/2-cos(5π/12+2θ)
收起