已知关于x的方程cos2x-2sinx+2a+1=0在区间(0,π/2]内有解,求实数a的取值范围

cos2x-2sinx+2a+1=01-2(sinx)^2-2sinx+2a+1=02(sinx)^2+2sinx=2a+2(sinx)^2+sinx=a+1(sinx)^2+sinx+1/4=a+1+1/4=a+5/4(sinx+1/2)^2=a+5/4因为方程cos2x-2sinx+2a+1=0在区间(0,π/2]内有解所以sinx在区间(0,π/2]内是...