Help with trigonometric problem?

Question

What is the lowest value for 2+ sinx cosx

Answer 1

2+sin x cos x= 2+1/2 cos 2x. When 2x = pi, the minimum value is 3/2.

Answer 2

sinx*cosx = -½ and +½ and all values between.

2 - ½ = 1½ <<<<<