We know that vector a = (cos3 / 2x, SIN3 / 2x), vector b = (cosx / 2, - SiNx / 2), and 0 The second question f (x) = (vector a dot multiplied by vector b) - 2 times m multiplied by (absolute value of a + b) The minimum value of F (x) is - 3 / 2, and the value of real number m is obtained

We know that vector a = (cos3 / 2x, SIN3 / 2x), vector b = (cosx / 2, - SiNx / 2), and 0 The second question f (x) = (vector a dot multiplied by vector b) - 2 times m multiplied by (absolute value of a + b) The minimum value of F (x) is - 3 / 2, and the value of real number m is obtained

a+b=(cos3/2x,sin3/2x)+(cosx/2,-sinx/2)
=(cos3/2x+cosx/2,sin3/2x-sinx/2)
|A + B | = radical [2 + 2 (cos3 / 2x * cosx / 2-sin3 / 2x * SiNx / 2)]
=Radical [2 + 2cos (3 / 2x + X / 2)]