Question

How do you find all solutions if 0 ≤ θ < 2π for `sin x cos 2x + cos x sin 2x = 1/2`?

Answer 1

Solve trig equation.

Ans: `pi/18 and (5pi)/18`

Explanation:

Apply the trig identity: sin a.cos b + sin b.cos a = sin (a + b).
sin (x + 2x) = sin 3x = 1/2
Trig table of special arcs -->
sin 3x = 1/2 --> 3x = pi/6 and 3x = (5pi)/6
a. `3x = pi/6` --> `x = pi/18`
b. `3x = (5pi)/6` --> `x = (5pi)/18`