How do you evaluate $cos (\frac{7 π}{3} + \frac{15 π}{4})$ $cos ((7 pi)/3 + (15 pi)/4)$ ?

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Answer 1 · 2016-06-04T16:57:04

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

$cos (\frac{7 π}{3} + \frac{15 π}{4})$ $cos ((7pi)/3+(15pi)/4)$

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

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

$= cos (\frac{π}{3} - \frac{π}{4})$ $=cos (pi/3-pi/4)$

$= cos (\frac{π}{3}) cos (\frac{π}{4}) + sin (\frac{π}{3}) sin (\frac{π}{4})$ $=cos(pi/3)cos(pi/4)+sin(pi/3)sin(pi/4)$

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

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

How do you evaluate cos ((7 pi)/3 + (15 pi)/4)cos(7π3+15π4)cos ((7 pi)/3 + (15 pi)/4)?