Question:
If \(\sin^{-1}(\frac{2a}{1+a^2})+\cos^{-1}(\frac{1-a^2}{1+a^2})=\tan^{-1}(\frac{2x}{1-x^2})\) where a, x ∈ (0, 1) then the value of x is
If \(\sin^{-1}(\frac{2a}{1+a^2})+\cos^{-1}(\frac{1-a^2}{1+a^2})=\tan^{-1}(\frac{2x}{1-x^2})\) where a, x ∈ (0, 1) then the value of x is
Updated On: Apr 17, 2024
- \(\frac{2a}{1+a^2}\)
- 0
- \(\frac{2a}{1-a^2}\)
- \(\frac{a}{2}\)
Hide Solution
Verified By Collegedunia
The Correct Option is C
Solution and Explanation
The correct answer is (C) : \(\frac{2a}{1-a^2}\).
Was this answer helpful?
0
0
Top Questions on Inverse Trigonometric Functions
- If the domain of the function \[\sin^{-1} \left( \frac{3x - 22}{2x - 19} \right) + \log_e \left( \frac{3x^2 - 8x + 5}{x^2 - 3x - 10} \right)\] is \( (\alpha, \beta] \), then \( 3\alpha + 10\beta \) is equal to:
- JEE Main - 2024
- Mathematics
- Inverse Trigonometric Functions
- Given the inverse trigonometric function assumes principal values only. Let \( x, y \) be any two real numbers in \( [-1, 1] \) such that \[ \cos^{-1}x - \sin^{-1}y = \alpha, \, -\frac{\pi}{2} \leq \alpha \leq \pi. \] Then, the minimum value of \( x^2 + y^2 + 2xy \sin \alpha \) is:
- JEE Main - 2024
- Mathematics
- Inverse Trigonometric Functions
- If the domain of the function \(f(x) = \sin^{-1}\left( \frac{x - 1}{2x + 3} \right)\) is \(\mathbb{R} - (\alpha, \beta)\), then \(12 \alpha \beta\) is equal to:
- JEE Main - 2024
- Mathematics
- Inverse Trigonometric Functions
- Let the inverse trigonometric functions take principal values. The number of real solutions of the equation \[ 2 \sin^{-1} x + 3 \cos^{-1} x = \frac{2\pi}{5}, \] is ______ .
- JEE Main - 2024
- Mathematics
- Inverse Trigonometric Functions
- Considering only the principal values of inverse trigonometric functions, the number of positive real values of \( x \) satisfying \[ \tan^{-1}(x) + \tan^{-1}(2x) = \frac{\pi}{4} \] is:
- JEE Main - 2024
- Mathematics
- Inverse Trigonometric Functions
View More Questions
Questions Asked in KCET exam
- The speed of sound in an ideal gas at a given temperature T is v. The rms speed of gas molecules at that temperature is vrms. The ratio of the velocities v and vrms for helium and oxygen gases are X and X' respectively. Then \(\frac{X}{X'}\) is equal to
- KCET - 2023
- Thermodynamics
- If \(p(\frac{1}{q}+\frac{1}{r}),q(\frac{1}{r}+\frac{1}{p}),r(\frac{1}{p}+\frac{1}{q})\) are in A.P., then p, q, r
- KCET - 2023
- Arithmetic Progression
- A stretched wire of a material whose Young's modulus Y = 2 × 1011 Nm-2 has Poisson's ratio of 0.25. Its lateral strain εl = 10-3. The elastic energy density of the wire is
- KCET - 2023
- mechanical properties of solids
- A metallic rod of length 1 m held along east-west direction is allowed to fall down freely. Given horizontal component of earth’s magnetic field BH = 3 × 10-5 T. The emf induced in the rod at an instant t = 2s after it is released is ( Take g = 10 ms-2 )
- KCET - 2023
- Faradays laws of induction
- A 60 W source emits monochromatic light of wavelength 662.5 nm. The number of photons emitted per second is
- KCET - 2023
- Quantum Physics
View More Questions