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\cot(\frac{\pi }{2}+\frac{\pi }{4})=\frac{\cot(\frac{\pi }{2})\cot(\frac{\pi }{4})-1}{\cot(\frac{\pi }{4})+\cot(\frac{\pi }{2})}
Use \cot(x+y)=\frac{\cot(x)\cot(y)-1}{\cot(y)+\cot(x)} where x=\frac{\pi }{2} and y=\frac{\pi }{4} to obtain the result.
\frac{0\cot(\frac{\pi }{4})-1}{\cot(\frac{\pi }{4})+0}
Get the value of \cot(\frac{\pi }{2}) from trigonometric values table. Replace the value in both the numerator and the denominator.
\frac{0\times 1-1}{1+0}
Get the value of \cot(\frac{\pi }{4}) from trigonometric values table. Replace the value in both the numerator and the denominator.
-1
Do the calculations.
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