NTA Abhyas JEE Main2020MathematicsInverse Trigonometric FunctionsPractice

If s i n - 1 5 x + s i n - 1 12 x = s i n - 1 2 x + c o s - 1 2 x , then the value of x is equal to

Correct answer

Step-by-step solution

s i n - 1 5 x and s i n - 1 12 x are both defined when x > 12 . Therefore c o s - 1 1 - 25 x 2 + s i n - 1 12 x = π 2 ∵ s i n - 1 2 x + c o s - 1 2 x = π 2 s i n - 1 12 x = s i n - 1 1 - 25 x 2 On comparing, we get, 12 x = 1 - 25 x 2 Therefore, 144 = x 2 - 25 or x = 1 3

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