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: $1$
Answer (1)
15th Jan, 2024
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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