Question

Find acute angles $A$ and $B$, if $\sin (A+B)=1$ and $\cos (A-B)=1$.

Answer 1

Given,

$\sin (A+B)=1\Rightarrow A+B={90}^o$......(1).

And $\cos (A-B)=1\Rightarrow A-B=0^o$ or $A=B$.....(2).

Solving from (1) and (2) we get,

$A=B={45}^o$.