How do you simplify cos (5pi/12)+cos(2pi/3-pi/4)?

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Answer 1 · 2016-10-07T10:33:32

$cos (\frac{5 π}{12}) + cos (\frac{2 π}{3} - \frac{π}{4})$ $cos( (5pi)/12)+cos((2pi)/3-pi/4)$

$= cos (\frac{5 π}{12}) + cos (\frac{8 π - 3 π}{12})$ $=cos( (5pi)/12)+cos((8pi-3pi)/12)$

$= 2 cos (\frac{5 π}{12})$ $=2cos( (5pi)/12)$

$= 2 \sqrt{\frac{1}{2} (1 + cos (\frac{5 π}{6}))}$ $=2 sqrt (1/2(1+cos( (5pi)/6))$

$= \sqrt{4 \times \frac{1}{2} (1 + cos (π - \frac{π}{6}))}$ $=sqrt (4xx1/2(1+cos(pi-pi/6))$

$= \sqrt{2 (1 - cos (\frac{π}{6}))}$ $=sqrt (2(1-cos(pi/6))$

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

$= \sqrt{2 - \sqrt{3}}$ $= sqrt(2-sqrt3)$

$= \sqrt{\frac{1}{2} (4 - 2 \sqrt{3})}$ $= sqrt(1/2(4-2sqrt3))$

$= \sqrt{\frac{1}{2} ({(\sqrt{3})}^{2} + 1^{2} - 2 \sqrt{3} \cdot 1)}$ $= sqrt(1/2((sqrt3)^2+1^2-2sqrt3*1))$

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

$= \frac{(\sqrt{3} - 1)}{\sqrt{2}}$ $= ((sqrt3-1))/sqrt2$