How do you simplify $4 cos (x + \frac{π}{3})$ $4cos(x+pi/3)$ ?

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How do you simplify $4 cos (x + \frac{π}{3})$ $4cos(x+pi/3)$ ?

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Answer 1 · 2018-05-04T04:29:42

$\Rightarrow 2 (cos x - \sqrt{3} sin x)$ $color(indigo)(=> 2 (cos x - sqrt3 sin x)$

Explanation:

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

$4 cos (x + (\frac{π}{3}))$ $4 cos (x + (pi/3))$

$\Rightarrow 4 (cos x cos (\frac{π}{3}) - sin x sin (\frac{π}{3}))$ $=> 4 (cosx cos (pi/3) - sinx sin (pi/3))$

$\Rightarrow 4 \cdot (\frac{cos x}{2} - \frac{\sqrt{3} sin x}{2}), as cos (\frac{π}{3}) = \frac{1}{2}, sin (\frac{π}{3}) = \frac{\sqrt{3}}{2}$ $=> 4 * (cos x/2 - (sqrt3 sin x) / 2), color(crimson)(" as " cos (pi/3) = 1/2, sin (pi/3) = sqrt3/2$

$\Rightarrow 2 (cos x - \sqrt{3} sin x)$ $color(indigo)(=> 2 (cos x - sqrt3 sin x)$

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How do you simplify $4 cos (x + \frac{π}{3})$ $4cos(x+pi/3)$ ?

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How do you simplify $4 cos (x + \frac{π}{3})$ $4cos(x+pi/3)$ ?