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