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

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