JEE Mains · Maths · STD 12 - 2. inverse trigonometric function
\(\tan \left(2 \tan ^{-1} \frac{1}{5}+\sec ^{-1} \frac{\sqrt{5}}{2}+2 \tan ^{-1} \frac{1}{8}\right)\) is equal to.
- A \(1\)
- B \(2\)
- C \(\frac{1}{4}\)
- D \(\frac{5}{4}\)
Answer & Solution
Correct Answer
(B) \(2\)
Step-by-step Solution
Detailed explanation
\(\tan \left(2\left(\tan ^{-1} \frac{1}{5}+\tan ^{-1} \frac{1}{8}\right)+\tan ^{-1}\left(\frac{1}{2}\right)\right)\) \(=\tan \left[2 \tan ^{-1}\left(\frac{1}{3}\right)+\tan ^{-1}\left(\frac{1}{2}\right)\right]\) \(=2\)
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 region represented by \(\left| {x - y} \right| \leq 2\) and \(\left| {x + y} \right| \leq 2\) is bounded by aJEE Mains 2019 Hard
- A man throws a fair coin repeatedly. He gets \(10\) points for each head he throws and \(5\) points for each tail he throws. If the probability that he gets exactly \(30\) points is \(\dfrac{m}{n}\), \(\gcd(m, n) = 1\), then \(m + n\) is equal to:JEE Mains 2026 Hard
- If for the complex numbers \(z\) satisfying \(|z-2-2 i| \leq 1\), the maximum value of \(|3 i z+6|\) is attained at \(\mathrm{a}+i \mathrm{~b}\), then \(\mathrm{a}+\mathrm{b}\) is equal to .... .JEE Mains 2021 Hard
- If the foci of a hyperbola are same as that of the ellipse \(\frac{x^2}{9}+\frac{y^2}{25}=1\) and the eccentricity of the hyperbola is \(\frac{15}{8}\) times the eccentricity of the ellipse, then the smaller focal distance of the point \(\left(\sqrt{2}, \frac{14}{3} \sqrt{\frac{2}{5}}\right)\) on the hyperbola, is equal toJEE Mains 2024 Hard
- Suppose that two chords, drawn from the point \((1, 2)\) on the circle \(x^2 + y^2 + x - 3y = 0\) are bisected by the \(y\)-axis. If the other ends of these chords are \(R\) and \(S\), and the mid point of the line segment \(RS\) is \((\alpha, \beta)\), then \(6(\alpha + \beta)\) is equal to:JEE Mains 2026 Medium
- Let the line passing through the points, \(P(2,-1,2)\) and \(Q(5,3,4)\) meet the plane \(x-y+z=4\) at the point \(R\). Then the distance of the point \(R\) from the plane \(x+2 y+3 z+2=0\) measured parallel to the line \(\frac{x-7}{2}=\frac{y+3}{2}=\frac{z-2}{1}\) is equal toJEE Mains 2023 Hard
More PYQs from JEE Mains
- Let \(A\) be a matrix of order \(3 \times 3\) and det \((A)=2\). Then \(\operatorname{det}\left(\operatorname{det}( A )\right.\) adj \(\left(5 \operatorname{adj}\left( A ^{3}\right)\right)\) ) is equal to.....JEE Mains 2022 Hard
- A line passes through \(A(4,-6,-2)\) and \(B(16,-2,4)\). The point \(\mathrm{P}(\mathrm{a}, \mathrm{b}, \mathrm{c})\) where \(\mathrm{a}, \mathrm{b}, \mathrm{c}\) are non-negative integers, on the line \(\mathrm{AB}\) lies at a distance of 21 units, from the point \(\mathrm{A}\). The distance between the points \(\mathrm{P}(\mathrm{a}, \mathrm{b}, \mathrm{c})\) and \(\mathrm{Q}(4,-12,3)\) is equal to ...........JEE Mains 2024 Medium
- The distance of the point \(P(3,4,4)\) from the point of intersection of the line joining the points \(\mathrm{Q}(3,-4,-5)\) and \(\mathrm{R}(2,-3,1)\) and the plane \(2 \mathrm{x}+\mathrm{y}+\mathrm{z}=7\), is equal to \(.....\)JEE Mains 2021 Medium
- Two integers \(\mathrm{x}\) and \(\mathrm{y}\) are chosen with replacement from the set \(\{0,1,2,3, \ldots ., 10\}\). Then the probability that \(|x-y|>5\) is :JEE Mains 2024 Hard
- The probability of a man hitting a target is \(\frac{2}{5}\). He fires at the target \(k\, times\) (\(k\), a given number). Then the minimum \(k\), so that the probability of hitting the target at least once is more than \(\frac{7}{10}\), isJEE Mains 2013 Hard
- If \(x \phi(x)=\int_{5}^{x}\left(3 t^{2}-2 \phi^{\prime}(t)\right) d t, x\,>\,-2\), and \(\phi(0)=4\) then \(\phi(2)\) is .... .JEE Mains 2021 Hard