cos A and sec A are reciprocal to each other.

Let x = cos A

then sec A = 1/cos A = 1/x

Let, cos A + sec A = 3/2

=> x + 1/x = 3/2

=> (x² + 1)/x = 3/2

=> 2(x² + 1) = 3x

=> 2(x² + 1) - 3x = 0

=> 2x² + 2 - 3x = 0

=> 2x² - 3x + 2 = 0

Now discriminant D = √(b² - 4*a*c)

=> D = √{(-3)² - 4*2*2)

=> D = √{9 - 16)

=> D = √(-7)

Since discriminant is negative, So there is no real roots of this quadratic equation.

Therefore cos A + sec A can not be equal to 3/2