The number of roots of the equation s i n - 1 x - c o s - 1 x = s i n - 1 5 x - 3 is/are

Step-by-step solution

s i n - 1 x - c o s - 1 x = s i n - 1 5 x - 3 ⇒ π 2 - c o s - 1 x - c o s - 1 x = π 2 - c o s - 1 5 x - 3 ⇒ 2 c o s - 1 x = c o s - 1 5 x - 3 . Also x ∈ - 1,1 … 1 ⇒ c o s - 1 2 x 2 - 1 = c o s - 1 5 x - 3 and 5 x - 3 ∈ - 1,1 , i.e., - 1 ≤ 5 x - 3 ≤ 1 ⇒ 2 x 2 - 1 = 5 x - 3 , h e n c e , x ∈ 2 5 , 4 5 ⇒ 2 x 2 - 5 x + 2 = 0 ⇒ x = 2 or 1 2 but, x = 2 does not satisfy the equation 1 Hence, the given equation has only one root