Find the value of cos5π/12?

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Find the value of cos5π/12?

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Answer 1 · 2018-06-12T10:47:25

$\frac{1}{4} (\sqrt{6} - \sqrt{2})$ $1/4(sqrt6-sqrt2)$

Explanation:

$using the trigonometric identity$ $"using the "color(blue)"trigonometric identity"$

$∙ x cos (x + y) = cos x cos y - sin x sin y$ $•color(white)(x)cos(x+y)=cosxcosy-sinxsiny$

$note that \frac{5 π}{12} = \frac{π}{6} + \frac{π}{4}$ $"note that "(5pi)/12=pi/6+pi/4$

$cos (\frac{5 π}{12}) = cos (\frac{π}{6} + \frac{π}{4})$ $cos((5pi)/12)=cos(pi/6+pi/4)$

$= cos (\frac{π}{6}) cos (\frac{π}{4}) - sin (\frac{π}{6}) sin π (/ 4)$ $=cos(pi/6)cos(pi/4)-sin(pi/6)sinpi(/4)$

$= (\frac{\sqrt{3}}{2} \times \frac{\sqrt{2}}{2}) - (\frac{1}{2} \times \frac{\sqrt{2}}{2})$ $=(sqrt3/2xxsqrt2/2)-(1/2xxsqrt2/2)$

$= \frac{\sqrt{6}}{4} - \frac{\sqrt{2}}{4} = \frac{1}{4} (\sqrt{6} - \sqrt{2})$ $=sqrt6/4-sqrt2/4=1/4(sqrt6-sqrt2)$

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Find the value of cos5π/12?

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