All the pairs ( x ,   y ) , that satisfy the inequality 2 s i n 2 x - 2 s i n x + 5 · 1 4 s i n 2 y ≤ 1 also satisfy the equation:

Question

All the pairs ( x , &#160; y ) , that satisfy the inequality 2 s i n 2 x - 2 s i n x + 5 &#183; 1 4 s i n 2 y &#8804; 1 also satisfy the equation:

Aicharya · Accepted Answer

Given inequality is 2 sin 2 &#8289; x - 2 sin &#8289; x + 5 &#160; &#8804; 4 sin 2 &#8289; y &#8658; sin 2 &#8289; x - 2 sin &#8289; x + 1 + 4 &#8804; 2 sin 2 &#8289; y &#8658; sin &#8289; x - 1 2 + 4 &#8804; 2 sin 2 &#8289; y &#8757; 2 sin 2 &#8289; y &#8712; 0 , &#160; 2 &#160; &#160; &#38; &#160; &#160; sin &#8289; x - 1 2 + 4 &#8712; 2 , &#160; 2 2 &#8757; &#160; Only equality holds &#8658; sin &#8289; x - 1 2 + 4 = 2 sin 2 &#8289; y = 2 &#8658; sin &#8289; x - 1 2 + 4 = 4 sin 4 &#8289; y = 4 &#160; &#8658; sin 2 &#8289; y = 1 &#160; &#160; &#160; &#8658; &#160; &#160; sin &#8289; y = 1 &#160; &#160; &#160; &#38; &#160; &#160; sin &#8289; x - 1 2 = 0 &#8658; sin &#8289; x = 1 &#8756; sin &#8289; y = sin &#8289; x

All the pairs ( x ,   y ) , that satisfy the inequality 2 s i n 2 x - 2 s i n x + 5 · 1 4 s i n 2…

Solution

All the pairs ( x , &#160; y ) , that satisfy the inequality 2 s i n 2 x - 2 s i n x + 5 &#183; 1 4 s i n 2…

Solution

All the pairs ( x , y ) , that satisfy the inequality 2 s i n 2 x - 2 s i n x + 5 · 1 4 s i n 2…