JEE Mains · Maths · STD 12 - 5. continuity and differentiation
The derivative of \({\tan ^{ - 1}}\left( {\frac{{\sin \,x - \cos \,x}}{{\sin \,x + \cos \,x}}} \right)\), with respect to \(\frac{x}{2}\), where \(\left( {x \in \left( {0,\frac{\pi }{2}} \right)} \right)\) is
- A \(2\)
- B \(\frac{1}{2}\)
- C \(1\)
- D \(\frac{2}{3}\)
Answer & Solution
Correct Answer
(A) \(2\)
Step-by-step Solution
Detailed explanation
Given \(y = {\tan ^{ - 1}}\left( {\frac{{\sin x - \cos x}}{{\sin x + \cos x}}} \right)\) \( \Rightarrow y = {\tan ^{ - 1}}\left( {\frac{{\tan x - 1}}{{\tan x + 1}}} \right)\) \( \Rightarrow y = - {\tan ^{ - 1}}\left( {\frac{{1 - \tan x}}{{1 + \tan x}}} \right)\)…
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
- An urn contains \(5\) red marbles, \(4\) black marbles and \(3\) white marbles. Then the number of ways in which \(4\) marbles can be drawn so that at the most three of them are red isJEE Mains 2020 Medium
- Let \(\omega \) be a complex number such that \(2\omega + 1 = z\) where \(z = \sqrt { - 3} \) . If \(\left| {\begin{array}{*{20}{c}}1&1&1\\1&{ - {\omega ^2} - 1}&{{\omega ^2}}\\1&{{\omega ^2}}&{{\omega ^7}}\end{array}} \right| = 3k\) then \(k\) is equal to :JEE Mains 2017 Hard
- The function, \(f(x)=(3 x-7) x^{2 / 3}, x \in R,\) is increasing for all \(x\) lying inJEE Mains 2020 Hard
- The equation of the normal to the curve \(y=(1+x)^{2 y}+\cos ^{2}\left(\sin ^{-1} x\right)\) at \(x=0\) isJEE Mains 2020 Hard
- 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
- The sum of all rational terms in the expansion of \(\left(1+2^{1 / 3}+3^{1 / 2}\right)^6\) is equal toJEE Mains 2025 Easy
More PYQs from JEE Mains
- The integral \(\int_{\pi /6}^{\pi /4} {\frac{{dx}}{{\sin \,2x\,\left( {{{\tan }^5}\,x + {{\cot }^5}\,x} \right)}}} \) equalsJEE Mains 2019 Hard
- Let \(\left\{a_{n}\right\}_{n=0}^{\infty}\) be a sequence such that \(a _{0}= a _{1}=0\) and \(a _{ n +2}=2 a _{ n +1}- a _{ n }+1\) for all \(n \geq 0\). Then, \(\sum\limits_{ n =2}^{\infty} \frac{ a _{ n }}{7^{ n }}\) is equal toJEE Mains 2022 Hard
- Let \(S = \{ x \in R:x \ge 0\) and \(2\left| {\sqrt x - 3} \right| + \sqrt x \left( {\sqrt x - 6} \right) + 6 = 0\} \) then \(S:\) . . .JEE Mains 2018 Hard
- The area of the quadrilateral \(ABCD\) with vertices \(A (2,1,1), B (1,2,5), C (-2,-3,5)\) and \(D (1,-6,-\) 7) is equal toJEE Mains 2023 Hard
- Let \(A = \{1, 4, 7\}\) and \(B = \{2, 3, 8\}\). Then the number of elements, in the relation \(R = \{((a_1, b_1), (a_2, b_2)) \in ((A \times B) \times (A \times B)) : a_1 + b_2 \text{ divides } a_2 + b_1\}\) is _______.JEE Mains 2026 Hard
- Let \(N\) be the sum of the numbers appeared when two fair dice are rolled and let the probability that \(N -2, \sqrt{3 N }, N +2\) are in geometric progression be \(\frac{ k }{48}\). Then the value of \(k\) isJEE Mains 2023 Hard