1/tanα+1/cotα=5/2,求2sin*2(3π-α）-3cos(π/2+α)cos(3π/2-α)+2的值
问题描述：
1/tanα+1/cotα=5/2,求2sin*2(3π-α）-3cos(π/2+α)cos(3π/2-α)+2的值
答
1/tanα+1/cotα=5/2
tanα=2或1/2
sin*2(3π-α）-3cos(π/2+α)cos(3π/2-α)+2
=2sin*2(α）-3cos(α)sin(-α)+2
=[2sin*2(α）+3cos(α)sin(α)]/(sin*2（α）+cos*2(α）)+ 2
=[2tan*2(α）+3tan(α）]/(tan*2（α）+1) +2
当tanα=2时,原式= 24/5
当tanα=1/2时,原式=18/5