Evaluate
\frac{\sqrt{\sqrt{2}+2}}{2}\approx 0.923879533
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\sin(\pi +\frac{\pi }{4})=\sin(\pi )\cos(\frac{\pi }{4})+\sin(\frac{\pi }{4})\cos(\pi )
Use \sin(x+y)=\sin(x)\cos(y)+\sin(y)\cos(x) where x=\pi and y=\frac{\pi }{4} to obtain the result.
0\cos(\frac{\pi }{4})+\sin(\frac{\pi }{4})\cos(\pi )
Get the value of \sin(\pi ) from trigonometric values table.
0\times \frac{\sqrt{2}}{2}+\sin(\frac{\pi }{4})\cos(\pi )
Get the value of \cos(\frac{\pi }{4}) from trigonometric values table.
0\times \frac{\sqrt{2}}{2}+\frac{\sqrt{2}}{2}\cos(\pi )
Get the value of \sin(\frac{\pi }{4}) from trigonometric values table.
0\times \frac{\sqrt{2}}{2}+\frac{\sqrt{2}}{2}\left(-1\right)
Get the value of \cos(\pi ) from trigonometric values table.
-\frac{\sqrt{2}}{2}
Do the calculations.
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