MHT CET · Maths · Inverse Trigonometric Functions
If \(\tan ^{-1}\left(\frac{1-x}{1+x}\right)=\frac{1}{2} \tan ^{-1} x\), then \(x\) is
- A \(1\)
- B \(\sqrt{3}\)
- C \(\frac{1}{\sqrt{3}}\)
- D \(\frac{1}{2 \sqrt{3}}\)
Answer & Solution
Correct Answer
(C) \(\frac{1}{\sqrt{3}}\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & \tan ^{-1}\left(\frac{1-x}{1+x}\right)=\frac{1}{2} \tan ^{-1} x \\ & \Rightarrow \tan ^{-1}(1)-\tan ^{-1}(x)=\frac{1}{2} \tan ^{-1} x \\ & \Rightarrow \frac{\pi}{4}=\frac{3}{2} \tan ^{-1} x \\ & \Rightarrow x=\tan \left(\frac{\pi}{6}\right)=\frac{1}{\sqrt{3}}\end{aligned}\)
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Maths
- The d.r.s. of the normal to the plane passing through the origin and the line of intersection of the planes \(x+2 y+3 z=4\) and \(4 x+3 y+2 z=1\) areMHT CET 2021 Medium
- The lines \(\overline{\mathrm{r}}=\bar{a}+\lambda(\overline{\mathrm{b}} \times \overline{\mathrm{c}})\) and \(\overline{\mathrm{r}}=\overline{\mathrm{c}}+\lambda(\bar{a} \times \overline{\mathrm{b}})\) will intersect ifMHT CET 2025 Medium
- \(\int x^2 \cos x \mathrm{~d} x=\)MHT CET 2025 Medium
- If \(\mathrm{A}=\left[\begin{array}{ll}\mathrm{i} & 1 \\ 1 & 0\end{array}\right]\) where \(\mathrm{i}=\sqrt{-1}\) and \(\mathrm{B}=\mathrm{A}^{2029}\), then \(\mathrm{B}^{-1}=\)MHT CET 2023 Easy
- If \(A=\left[\begin{array}{cc}2 & -1 \\ -1 & 2\end{array}\right]\) such that \(A^2-4 A+3 I=0\), where \(\mathrm{I}\) is a unit matrix of order 2 , then \(A^{-1}\) isMHT CET 2022 Medium
- If the slope of one of the lines given by \(\mathrm{K} x^2+6 x y+y^2=0\) is three times the order, then the value of K isMHT CET 2024 Medium
More PYQs from MHT CET
- A heavy mass is attached at one end of a thin wire and whirled in a vertical circle. The chances of breaking the wire are maximum whenMHT CET 2020 Medium
- The 1. Order and Degree of differential equation of all tangent lines to the parabola \(x^2=4 \mathrm{y}\) is respectively.MHT CET 2025 Medium
- Domain of the real valued function \(f(x)=\frac{x+2}{9-x^{2}}\) isMHT CET 2020 Easy
- In Lyman series, series limit of wavelength is \(\lambda_1\). The wavelength of first line of Lyman series is \(\lambda_2\) and in Balmer series, the series limit of wavelength is \(\lambda_3\). Then the relation between \(\lambda_1\), \(\lambda_2\) and \(\lambda_3\) isMHT CET 2023 Easy
- Let A and B be two events such that the probability that exactly one of them occurs is \(\frac{2}{5}\) and the probability that A or B occurs is \(\frac{1}{2}\), then the probability of both of them occur together isMHT CET 2024 Medium
- Which of the following does not have intermolecular hydrogen bonding?MHT CET 2024 Easy