If sin(x-y)=cos(x+y)=1/2,then the values of x and y lying b/w 0° and 180° are given by

a.x=45°,y=45°

b.x=45°,y=135°

c.x=165°,y=15°

d.x=165°,y=135°

x-y=nπ+ (-1)ⁿsin^-1(1/2), x+y=2mπ±cos^-1(1/2), n and m are both integers

it is d. x=165,y=135

Hi Menka,

To solve this question quickly, first note that 0 <= x,y <= 180.

So min (x-y) = -180, and max (x-y) = 180

and min (x+y) = 0 and max (x+y) = 360

This is the interval where you need to be looking for solutions:

so x-y = 30 or 150

and x+y = 60 or 300.

Clearly only option D satisfies.

Hope that helps.

All the best,

Regards,

Ashwin (IIT Madras).