Question

Find the acute angles $A$ and $B$ satisfying $\cot (A+B)=1,cosec(A-B)=2$.

Answer 1

$\cot (A+B)=1$

or, $A+B={45}^o$.....(1) [ Since $A,B$ are acute].

Again,

$cosec(A-B)=2$

or, $\sin (A-B)=\frac{1}{2}$

or, $A-B={30}^o$.....(2).

Now solving from (1) and (2) we get,

$A=\frac{{75}^o}{2}$ and $B=\frac{{15}^o}{2}$.