If sin - 1 x + sin - 1 y = 2 π 3 and cos - 1 x - cos - 1 y = π 3 .Then, ( x ,   y ) is equal to

Step-by-step solution

Given, sin - 1 x + sin - 1 y = 2 π 3       . . . ( i ) and cos - 1 x - cos - 1 y = π 3       . . . ( i i ) We know that sin - 1 x + cos - 1 x = π 2 Using the above concept, we can write ⇒ π 2 - sin - 1 x - π 2 - sin - 1 y = π 3 ⇒ - sin - 1 x + sin - 1 y = π 3       . . . ( i i i ) On adding equation i and i i i , we get sin - 1 y = π 2 ⇒ y = 1 On subtracting equation i from equation i i i , we get sin - 1 x = &#96