How do you verify the identity $cos (\frac{π}{3} + x) + cos (\frac{π}{3} - x) = cos x$ $cos(pi/3+x)+cos(pi/3-x)=cosx$ ?

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How do you verify the identity $cos (\frac{π}{3} + x) + cos (\frac{π}{3} - x) = cos x$ $cos(pi/3+x)+cos(pi/3-x)=cosx$ ?

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Answer 1 · 2017-10-07T08:22:35

Please refer to a Proof in the Explanation.

Explanation:

Using, $cos C + cos D = cos (\frac{C + D}{2}) cos (\frac{C - D}{2}),$ $cosC+cosD=cos((C+D)/2)cos((C-D)/2),$ we have,

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

$= 2 cos (\frac{1}{2}) {(\frac{π}{3} + x) + (\frac{π}{3} - x))} cos (\frac{1}{2}) {(\frac{π}{3} + x) - (\frac{π}{3} - x)},$ $=2cos(1/2){(pi/3+x)+(pi/3-x))}cos(1/2){(pi/3+x)-(pi/3-x)},$

$= 2 cos (\frac{π}{3}) cos x,$ $=2cos(pi/3)cosx,$

$= 2 \cdot \frac{1}{2} \cdot cos x,$ $=2*1/2*cosx,$

$= cos x .$ $=cosx.$

Hence, the Proof.

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How do you verify the identity $cos (\frac{π}{3} + x) + cos (\frac{π}{3} - x) = cos x$ $cos(pi/3+x)+cos(pi/3-x)=cosx$ ?

1 Answer

Explanation:

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