Given, sin‌x+sin‌y=a and cos‌x+cos‌y=b ⇒sin2x+sin2y+2‌sin‌x‌sin‌y=a2 (i) and cos2x+cos2y+2‌cos‌x‌cos‌y=b2 (ii) On adding Eqs. (i) and (ii), we get (sin2x+cos2x)+(sin2y+cos2y)+2(sin‌x‌sin‌y+cos‌x‌cos‌y)=a2+b2 ⇒sin‌x‌sin‌y+cos‌x‌cos‌y=