Question

How do you solve `sinx*cosx=1/2` for x in the interval [0,2pi)?

Answer 1

`x = pi/4`

Explanation:

Use trig identity: sin 2x = 2sin x.cos x
sin x.cos x = `(1/2)sin 2x = 1/2` --> sin 2x = 1
sin 2x = 1 --> arc `2x = pi/2` --> `x = pi/4`

Check
sin (pi/4).cos (pi)/4 = (sqrt2/2)(sqrt2/2) = 2/4 = 1/2 . OK