Exams › JEE Main › Maths

If cos⁻¹ ((2)/(3x))+cos⁻¹ ((3)/(4x))=(π)/(2), where x>(3)/(4), then the value of x is:

1. (√(145))/(12)
2. (√(145))/(10)
3. (√(146))/(12)
4. (√(145))/(11)

Correct answer: (√(145))/(12)

Solution

From cos^-1(2/3x)+cos^-1(3/4x)=pi/2, we get cos^-1(2/3x)=sin^-1(3/4x), so 2/(3x)=sqrt(1-9/(16x^2)). Squaring: 4/(9x^2)+9/(16x^2)=1 -> 145/(144x^2)=1 -> x=sqrt(145)/12.

Related JEE Main Maths questions

• For the function f(x) = log(x + √(x² + 1)), which of the following describes it correctly?
• For the function f(x) = log((1 + x)/(1 − x)), which of the following relations is satisfied?
• Find the domain of the function f(x)=sin⁻¹{log2(1/2 x²)}.
• For which values of x does the inequality sin⁻¹(sin 5) > x² − 4x hold?
• Determine the range of the function f(x) = sin⁻¹x + tan⁻¹x + sec⁻¹x.
• If A = tan⁻¹ ((x√(3))/(2K-x)) and B = tan⁻¹ ((2x-K)/(K√(3))), then what is the value of A - B?

⚔️ Practice JEE Main Maths free + battle 1v1 →