How do you find the exact value of $cos (\frac{π}{4} + \frac{π}{3})$ $cos(pi/4+pi/3)$ ?

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How do you find the exact value of $cos (\frac{π}{4} + \frac{π}{3})$ $cos(pi/4+pi/3)$ ?

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Answer 1 · 2017-09-23T08:16:01

$cos (\frac{π}{4} + \frac{π}{3}) = \frac{\sqrt{2} - \sqrt{6}}{4}$ $cos(pi/4+pi/3) = (sqrt2-sqrt6)/4$

Explanation:

In order to evaluate $cos (\frac{π}{4} + \frac{π}{3})$ $cos(pi/4+pi/3)$ we need to use the compound angle formula for cos: $cos (A + B) \equiv cos A cos B - sin A sin B$ $cos(A+B) -= cosAcosB-sinAsinB$

$therefore cos(pi/4+pi/3) = cos(pi/4)cos(pi/3)-sin(pi/4)sin(pi/3) = 1/sqrt2 *1/2 - 1/sqrt2*sqrt3/2 = 1/(2sqrt2)-sqrt3/(2sqrt2) = (1-sqrt3)/(2sqrt2)=(sqrt2-sqrt6)/4$

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How do you find the exact value of $cos (\frac{π}{4} + \frac{π}{3})$ $cos(pi/4+pi/3)$ ?

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How do you find the exact value of $cos (\frac{π}{4} + \frac{π}{3})$ $cos(pi/4+pi/3)$ ?