If sinx .cosy + cosx.siny = 1, then the value of x + y will be

Here,

$sin x cdot cos y+cos x cdot sin y=1$

$Rightarrow sin (x+y)=1$

[ sin (A + B) = sinA cosB + cosA sinB]

$Rightarrow sin (x+y)=sin frac{pi}{2}$

$Rightarrow x+y=frac{pi}{2}$