Question

If $\sin A=\frac{1}{\sqrt{2}}$ and $\cot B=1$, prove that $\sin (A+B)=1$, where $A$ and $B$ are acute angles.

Answer 1

Given, $\sin A=\frac{1}{\sqrt{2}}$

$\therefore A={45}^o$

$\cot B=1$

$\therefore B={45}^o$

Hence, $\sin (A+B)=\sin ({45}^o+{45}^o)$

$=\sin {90}^o$

$=1$