MHT CET · Maths · Inverse Trigonometric Functions
The number of solutions of
\(\tan ^{-1}\left(x+\frac{2}{x}\right)-\tan ^{-1}\left(\frac{4}{x}\right)-\tan ^{-1}\left(x-\frac{2}{x}\right)=0\) are
- A \(1\)
- B \(2\)
- C \(3\)
- D \(0\)
Answer & Solution
Correct Answer
(B) \(2\)
Step-by-step Solution
Detailed explanation
\(\tan ^{-1}\left(x+\frac{2}{x}\right)-\tan ^{-1}\left(\frac{4}{x}\right)=\tan ^{-1}\left(x-\frac{2}{x}\right)\) \(\tan ^{-1}\left(\frac{\left(x+\frac{2}{x}\right)-\frac{4}{x}}{1+\left(x+\frac{2}{x}\right)\left(\frac{4}{x}\right)}\right)=\tan ^{-1}\left(x-\frac{2}{x}\right)\)
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
- Let \(\overline{\mathrm{a}}, \overline{\mathrm{b}}\) and \(\overline{\mathrm{c}}\) be vectors of magnitude 2,3 and 4 respectively. If \(\bar{a}\) is perpendicular to \((\bar{b}+\bar{c}), \bar{b}\) is perpendicular to \((\bar{c}+\bar{a})\) and \(\vec{c}\) is perpendicular to \((\bar{a}+\bar{b})\), then the magnitude of \(\overline{\mathrm{a}}+\overline{\mathrm{b}}+\overline{\mathrm{c}}\) is equal toMHT CET 2024 Easy
- If \(y=\tan ^{-1}(\sec x-\tan x)\), then \(\frac{d y}{d x}=\)MHT CET 2022 Medium
- If \(x y=\tan ^{-1}(x y)+\cot ^{-1}(x y)\), then \(\left(\frac{\mathrm{d} y}{\mathrm{~d} x}\right)_{(4,2)}=(\) where \(x, y \in I R)\)MHT CET 2022 Medium
- If \(\bar{a}, \bar{b}, \bar{c}\) are mutually perpendicular vectors having magnitudes 1,2,3 respectively, then \([\overline{\mathrm{a}}+\overline{\mathrm{b}}+\overline{\mathrm{c}} \overline{\mathrm{b}}-\overline{\mathrm{a}} \overline{\mathrm{c}}]=\)MHT CET 2021 Medium
- If \(\overline{\mathrm{a}}, \overline{\mathrm{b}}\) and \(\overline{\mathrm{c}}\) are unit coplanar vectors, then the scalar triple product \(\left[\begin{array}{lll}2 \bar{a}-\bar{b} & 2 \bar{b}-\bar{c} & 2 \bar{c}-\bar{a}\end{array}\right]\) has the valueMHT CET 2024 Easy
- The equation of tangent to the curve \(y^{2}=a x^{2}+b\) at point \((2,3)\) is \(y=4 x-5\), then the values of \(a\) and \(\bar{b}\) areMHT CET 2010 Easy
More PYQs from MHT CET
- \(\int_0^{\frac{\pi}{4}} \frac{\cos ^2 x \sin ^2 x}{\left(\cos ^3 x+\sin ^3 x\right)^2} \mathrm{~d} x=\)MHT CET 2025 Medium
- Lymph does NOT contain __________ .MHT CET 2021 Medium
- Derivative of \(\tan ^{-1}\left(\frac{\sqrt{1+x^2}-\sqrt{1-x^2}}{\sqrt{1+x^2}+\sqrt{1-x^2}}\right)\) w.r.t. \(\cos ^{-1} x^2\) isMHT CET 2023 Hard
- The value of
\(\cos \left(18^{\circ}-\mathrm{A}\right) \cos \left(18^{\circ}+\mathrm{A}\right) \
-\cos \left(72^{\circ}-\mathrm{A}\right) \cos\) \(\left(72^{\circ}+\mathrm{A}\right)\) is equal toMHT CET 2024 Medium - The population of a village increases at a rate proportional to the population at that time. In a period of 10 years the population grew from 20,000 to 40,000 , then the population after another 20 years isMHT CET 2020 Medium
- A block of mass 'm' moving along a straight line with constant velocity \(3 \overrightarrow{\mathrm{V}}\) collides
with another block of same mass at rest. They stick together and move with
common velocity. The common velocity isMHT CET 2020 Easy