Question : If $\cot A=1, \sin B=\frac{1}{\sqrt{2}}$, find the value of $\sin (A+B)-\cot (A+B)$.
Option 1: $1-\sqrt{2}$
Option 2: $\frac{1}{2}$
Option 3: $0$
Option 4: $1$
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Correct Answer: $1$
Solution : $\cot A = 1= \cot 45°$ $\therefore A = 45°$ $\sin B = \frac{1}{\sqrt{2}}=\sin45°$ $\therefore B = 45°$ $\sin (A+B) = \sin 90° = 1$ $\cot (A+B) = \cot 90° = 0$ $\therefore \sin (A+B) -\cot (A+B) =1-0= 1$ Hence, the correct answer is $1$.
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