Question

How do you simplify `4cos(x+pi/3)`?

Answer 1

`color(indigo)(=> 2 (cos x - sqrt3 sin x)`

Explanation:

`cos (x + y) = cos x cos y - sin x sin y, color(crimson)("basic trigonometric identity"`

`4 cos (x + (pi/3))`

`=> 4 (cosx cos (pi/3) - sinx sin (pi/3))`

`=> 4 * (cos x/2 - (sqrt3 sin x) / 2), color(crimson)(" as " cos (pi/3) = 1/2, sin (pi/3) = sqrt3/2`

`color(indigo)(=> 2 (cos x - sqrt3 sin x)`