不懂算已知tanα=1/2,求1+2sin(π-α)cos(-2π-α)/sin²(-α)-sin²(5π/2 -α)的值
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![不懂算已知tanα=1/2,求1+2sin(π-α)cos(-2π-α)/sin²(-α)-sin²(5π/2 -α)的值](/uploads/image/z/2738551-31-1.jpg?t=%E4%B8%8D%E6%87%82%E7%AE%97%E5%B7%B2%E7%9F%A5tan%CE%B1%3D1%2F2%2C%E6%B1%821%2B2sin%28%CF%80-%CE%B1%29cos%28-2%CF%80-%CE%B1%29%2Fsin%26%23178%3B%28-%CE%B1%29-sin%26%23178%3B%285%CF%80%2F2+-%CE%B1%29%E7%9A%84%E5%80%BC)
不懂算已知tanα=1/2,求1+2sin(π-α)cos(-2π-α)/sin²(-α)-sin²(5π/2 -α)的值
不懂算已知tanα=1/2,求1+2sin(π-α)cos(-2π-α)/sin²(-α)-sin²(5π/2 -α)的值
不懂算已知tanα=1/2,求1+2sin(π-α)cos(-2π-α)/sin²(-α)-sin²(5π/2 -α)的值
解
1+2sin(π-α)cos(-2π-α)/sin²(-α)-sin²(5π/2 -α)
=1+2sinacos[-(2π+a)]/[sin²a-sin²(π/2-a)]
=(1+2sinacosa)/(sin²a-cos²a)
=(sin²a+cos²a+2sinacosa)/(sin²a-cos²a)——(分子分母除以cos²a)
=(tan²a+1+2tana)/(tan²a-1)
=(1/4+1+1)/(1/4-1)
=9/4*(-4/3)
=-3