How do you simplify $cos (π + x) + cos (π - x)$ $cos( pi + x) + cos (pi - x)$ ?

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How do you simplify $cos (π + x) + cos (π - x)$ $cos( pi + x) + cos (pi - x)$ ?

1 Answer

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Answer 1 · 2016-03-27T04:21:36

2cos x

Explanation:

Apply the trig identity:
$cos a + cos b = 2 cos (\frac{a + b}{2}) . cos (\frac{a - b}{2})$ $cos a + cos b = 2cos ((a + b)/2).cos ((a - b)/2)$
$S = cos (π + x) + cos (π - x) = 2 cos (π) . cos (- x)$ $S = cos (pi + x) + cos (pi - x) = 2cos (pi).cos (- x)$
Since $cos π = - 1$ $cos pi = - 1$ and $cos (- x) = cos x$ $cos (- x) = cos x$ , therefor
S = - 2cos x

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How do you simplify $cos (π + x) + cos (π - x)$ $cos( pi + x) + cos (pi - x)$ ?

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