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\cos(90+45)=\cos(90)\cos(45)-\sin(45)\sin(90)
Use \cos(x+y)=\cos(x)\cos(y)-\sin(y)\sin(x) where x=90 and y=45 to obtain the result.
0\cos(45)-\sin(45)\sin(90)
Get the value of \cos(90) from trigonometric values table.
0\times \frac{\sqrt{2}}{2}-\sin(45)\sin(90)
Get the value of \cos(45) from trigonometric values table.
0\times \frac{\sqrt{2}}{2}-\frac{\sqrt{2}}{2}\sin(90)
Get the value of \sin(45) from trigonometric values table.
0\times \frac{\sqrt{2}}{2}-\frac{\sqrt{2}}{2}\times 1
Get the value of \sin(90) from trigonometric values table.
-\frac{\sqrt{2}}{2}
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