If tan (x + y) = 1 and cos(x - y) = $\sqrt{3}/2$, then what is the value of x and y ?

x = 37.5, y = 7.5

We are given that ,

tan (x + y) = 1

{ tan 90º = 1 }

So, ( x + y ) = 90º      ----(1)

& cos ( x - y ) = \(\frac{ √ 3 }{2}\)

{ we know, cos30º = \(\frac{ √ 3 }{2}\) }

( x - y ) = 30º   ---(2)

On adding equation 1 and 2.

2x = 120º

x = 60º 

Now, 60º + y = 90º

y = 30º

Ans :-  x = 60º  &  y = 30º