If cos - 1 2 3 x + cos - 1 3 4 x = π 2 x > 3 4 , then x is equal to :

Step-by-step solution

We have, c o s - 1 2 3 x + c o s - 1 3 4 x = π 2 ,   x > 3 4       . . . i ∴   cos - 1 3 4 x = sin - 1 16 x 2 - 9 4 x Put in equation i we get, ⇒ c o s - 1 2 3 x + s i n - 1 16 x 2 - 9 4 x = π 2     . . . ii We know sin - 1 x + cos - 1 x = π 2 From equation ii we get, ⇒ 2 3 x = 16 x 2 - 9 4 x ⇒ 8 3 2 = 16 x 2 - 9     ∵   x ≠ 0 ⇒ 16 x 2 = 64 9 + 9 = 145 9 ⇒ x 2 = 145 144 ⇒ x = 145 12