JEE Mains · Maths · STD 12 - 2. inverse trigonometric function
If \(\sin(\tan^{-1}(x\sqrt{2})) = \cot(\sin^{-1}\sqrt{1-x^2})\), \(x \in (0,1)\), then the value of \(x\) is :
- A \(\dfrac{1}{2}\)
- B \(\dfrac{1}{3}\)
- C \(\dfrac{2}{3}\)
- D \(\dfrac{5}{8}\)
Answer & Solution
Correct Answer
(A) \(\dfrac{1}{2}\)
Step-by-step Solution
Detailed explanation
Let \(\alpha = \tan^{-1}(x\sqrt{2}) \Rightarrow \tan\alpha = x\sqrt{2}\) From the right-angled triangle, \(\sin\alpha = \dfrac{x\sqrt{2}}{\sqrt{1+2x^2}}\) Let \(\beta = \sin^{-1}\sqrt{1-x^2} \Rightarrow \sin\beta = \sqrt{1-x^2}\) From the right-angled triangle,…
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
- If for \(x \geq 0, y=y(x)\) is the solution of the differential equation \((\mathrm{x}+1) \mathrm{d} \mathrm{y}=\left((\mathrm{x}+1)^{2}+\mathrm{y}-3\right) \mathrm{d} \mathrm{x}, \mathrm{y}(2)=0\) then \(y(3)\) is equal toJEE Mains 2020 Hard
- The point of intersection of the normals to the parabola \(y^ 2\, = 4x\) at the ends of its latus rectum isJEE Mains 2013 Hard
- If \(\frac{{{}^{n + 2}{C_6}}}{{{}^{n - 2}{P_2}}} = 11\), then \(n\) satisfies the equationJEE Mains 2016 Hard
- If \(\alpha,-\frac{\pi}{2}<\alpha<\frac{\pi}{2}\) is the solution of \(4 \cos \theta+5 \sin \theta=1\), then the value of \(\tan \alpha\) isJEE Mains 2024 Medium
- The number of all \(3 \times 3\) matrices \(A\), with enteries from the set \(\{-1,0,1\}\) such that the sum of the diagonal elements of \(\mathrm{AA}^{\mathrm{T}}\) is \(3,\) isJEE Mains 2020 Hard
- Let the image of the point \(P(1, 6, a)\) in the line \(L: \dfrac{x}{1} = \dfrac{y-1}{2} = \dfrac{z-a+1}{b}\), \(b > 0\), be \(\left(\dfrac{a}{3}, 0, a+c\right)\). If \(S(\alpha, \beta, \gamma)\), \(\alpha > 0\), is the point on \(L\) such that the distance of \(S\) from the foot of perpendicular from the point \(P\) on \(L\) is \(2\sqrt{14}\), then \(\alpha + \beta + \gamma\) is equal to:JEE Mains 2026 Hard
More PYQs from JEE Mains
- The number of integral terms in the expansion of \(\left(5^{\frac{1}{2}}+7^{\frac{1}{8}}\right)^{1016}\) isJEE Mains 2025 Easy
- Let \(A=\left[\begin{array}{lll}1 & 0 & 0 \\ 0 & \alpha & \beta \\ 0 & \beta & \alpha\end{array}\right]\) and \(|2 A|^3=2^{21}\) where \(\alpha, \beta \in Z\), Then a value of \(\alpha \) isJEE Mains 2024 Hard
- Let \(y=y(x)\) be the solution of the differential equation \(x\frac{dy}{dx}-sin~2y=x^{3}(2-x^{3})cos^{2}y,\) \(x\ne0.\) If \(y(2)=x,\) then \(tan(y(1))\) is equal toJEE Mains 2026 Hard
- Let \(E_{1}\) and \(E_{2}\) be two events such that the conditional probabilities \(P \left( E _{1} \mid E _{2}\right)=\frac{1}{2}\), \(P \left( E _{2} \mid E _{1}\right)=\frac{3}{4}\) and \(P \left( E _{1} \cap E _{2}\right)=\frac{1}{8}\). ThenJEE Mains 2022 Hard
- If \(0\,<\,x\,<\,1\) and \(y=\frac{1}{2} x^{2}+\frac{2}{3} x^{3}+\frac{3}{4} x^{4}+\ldots\), then the value of \(\mathrm{e}^{1+y}\) at \(\mathrm{x}=\frac{1}{2}\) is:JEE Mains 2021 Hard
- Let a relation \(R\) on \(\mathbb{N} \times \mathbb{N}\) be defined as : \(\left(\mathrm{x}_1, \mathrm{y}_1\right) \mathrm{R}\left(\mathrm{x}_2, \mathrm{y}_2\right)\) if and only if \(\mathrm{x}_1 \leq \mathrm{x}_2\) or \(\mathrm{y}_1 \leq \mathrm{y}_2\) Consider the two statements : (\(I\)) \(\mathrm{R}\) is reflexive but not symmetric. (\(II\)) \(\mathrm{R}\) is transitive Then which one of the following is true?JEE Mains 2024 Medium