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: $1$

Question

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: $1$

Team Careers360 · Accepted Answer

Correct Answer: $1$

Solution : $\cot A = 1= \cot 45°$
$ herefore A = 45°$
$\sin B = \frac{1}{\sqrt{2}}=\sin45°$
$ herefore B = 45°$
$\sin (A+B) = \sin 90° = 1$
$\cot (A+B) = \cot 90° = 0$
$ herefore \sin (A+B) -\cot (A+B) =1-0= 1$
Hence, the correct answer is $1$.

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Question : If cot⁡A=1,sin⁡B=12, find the value of sin⁡(A+B)−cot⁡(A+B).Option 1: 1−2Option 2: 12Option 3: 0Option 4: 1

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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: $1$