Question

求（√3tan12°-3)/(sin12°X(4cos12°-2））的值

Answer 1

4(cos12)^2-2 =2[2(cos12)^2-1] =2cos24 所以分母=2cos24sin12 分子=√3*sin12/cos12-3 =(√3*sin12-3cos12)/cos12 所以原式=(√3*sin12-3cos12)/[cos12*2cos24sin12] =(√3*sin12-3cos12)/[(1/2)*sin48] =2(√3*sin12-3cos12)/sin48 =4√3[(1/2)sin12-√3/2*cos12)/sin48 =4√3(sin12cos60-cos12sin60)/sin48 =4√3(sin12-60)/sin48 =-4√3sin48/sin48 =-4√3