1.
[根號(hào)3(tan12°-根號(hào)3)]/[2sin12°(2cos平方12°-1)]
=(根號(hào)3tan12-3)/[2sin12cos24]
=[cos12(根號(hào)3tan12-3)]/[2sin12cos12cos24]
=(根號(hào)3sin12-3cos12)/[sin24cos24]
=(根號(hào)3sin12-3cos12)/[1/2sin48]
=(根號(hào)3sin12-3cos12)/[1/2sin(60-12)]
=(根號(hào)3sin12-3cos12)/[根號(hào)3/4cos12-1/4sin12]
=-(根號(hào)3)/4
2.
[根號(hào)(sin平方2x+cos平方x)]+sin2x+(根號(hào)3)*cos2x
=根號(hào)[(sin2x)^2+cos^2(x)]+sin2x+根號(hào)3cos2x
=根號(hào)[4sin^2(x)cos^2(x)+cos^2(x)]+(sin2x+根號(hào)3cos2x)
=根號(hào){cos^2(x)[4sin^2(x)+1]}+2sin(2x+pi/3)
=|cosx|根號(hào)[4sin^2(x)+1]+2sin(2x+pi/3)