Question

How do you solve `sin 2x cos x + cos 2x sin x = [sqrt 2]/2`?

Answer 1

Solve trig equation.

Ans: `pi/12` and `pi/4`

Explanation:

Use trig identity: `sin(a + b) = sin a cos b + sin b cos a`
`sin(2x + x) = sqrt2/2`
`sin 3x = sqrt2/2`
Trig table gives -->`3x = pi/4` --> `x = (pi)/12`
Trig unit circle gives another arc `3x = pi - pi/4 = (3pi)/4` -->
->`x = pi/4`