化简sin(π-a)tan(2π-a)cos(-a+3π/2)/tan(-π-a)cos(-π-a)(1)若cos(a+2π)=1/5求值(2)a=-1860度,求值
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![化简sin(π-a)tan(2π-a)cos(-a+3π/2)/tan(-π-a)cos(-π-a)(1)若cos(a+2π)=1/5求值(2)a=-1860度,求值](/uploads/image/z/1259784-0-4.jpg?t=%E5%8C%96%E7%AE%80sin%28%CF%80-a%29tan%282%CF%80-a%29cos%28-a%2B3%CF%80%2F2%29%2Ftan%28-%CF%80-a%29cos%28-%CF%80-a%29%EF%BC%881%EF%BC%89%E8%8B%A5cos%28a%2B2%CF%80%29%3D1%2F5%E6%B1%82%E5%80%BC%EF%BC%882%EF%BC%89a%3D-1860%E5%BA%A6%EF%BC%8C%E6%B1%82%E5%80%BC)
化简sin(π-a)tan(2π-a)cos(-a+3π/2)/tan(-π-a)cos(-π-a)(1)若cos(a+2π)=1/5求值(2)a=-1860度,求值
化简sin(π-a)tan(2π-a)cos(-a+3π/2)/tan(-π-a)cos(-π-a)
(1)若cos(a+2π)=1/5求值
(2)a=-1860度,求值
化简sin(π-a)tan(2π-a)cos(-a+3π/2)/tan(-π-a)cos(-π-a)(1)若cos(a+2π)=1/5求值(2)a=-1860度,求值
sin(π-a)tan(2π-a)cos(-a+3π/2)/tan(-π-a)cos(-π-a)
=[sinatan(-a)(-sina)]/[(-tana)(-cosa)]
=[sina(-tana)(-sina)]/(tanacosa)
=(sin^2atana)/(tanacosa)
=sin^2a/cosa
(奇变偶不变,符号看象限,可以先把a看做锐角)
(1)cos(a+2π)=1/5
cosa=1/5,由sin^2+cos^2a=1得sin^2a=24/25
将sin^2a=24/25,cosa=1/5代入上式得
原式=(24/25)/(1/5)=24/5
(2)a=-1860°=-31π/3=-10π-π/3(正余弦函数的最小正周期为2π,-10π当然也是其周期)
原式=sin^2(-31π/3)/cos(-31π/3)=sin^2(-π/3)/cos(-π/3)=sin^2(π/3)/cos(π/3)=(√3/2)^2/(1/2)=3/2
楼主自己检查下~
别人回答很对,采纳