The sum of all the values of x between 0 and 4 π which satisfy the equation s i n x 8 c o s 2 x = 1 is k π , then the value of k 5 is equal to

Step-by-step solution

Given equation is s i n x c o s 2 x = 1 2 2 ⇒ sin ⁡ x cos ⁡ x = 1 2 2 Case (I): When x > 0 i.e. x lies in 1 s t or 4 t h quadrant. sin ⁡ x cos ⁡ x = 1 2 2 ⇒ sin ⁡ 2 x = 1 2 ⇒ 2 x = π 4 , 3 π 4 , 9 π 4 , 11 π 4 , 17 π 4 , 19 π 4 ⇒ x = π 8 , 3 π 8 , 9 π 8 , 11 π 8 , 17 π 8 , 19 π 8 As x lies between 0 and 4 π , cos ⁡ x > 0 ⇒ x = π 8 , 3 π 8 , 17 π 8 , 19 π 8 Ca