Question

If $A$ and $B$ are acute angles and $\sin A=\cos B$, then find the value of $A+B$.

Answer 1

We know $\sin A=\cos (90-A)$

Given, $\sin A=\cos B$

$\cos B=\cos (90-A)$

$\Rightarrow B=90-A\Rightarrow A+B=90$

Hence, $A+B=90$