WBJEE · Maths · Differentiation
For \(-\frac{\pi}{2} < x < \frac{3 \pi}{2}, \quad\) the \(\quad\) value \(\quad\) of \(\frac{d}{d x}\left\{\tan ^{-1} \frac{\cos x}{1+\sin x}\right\}\) is equal to
- A \(\frac{1}{2}\)
- B \(-\frac{1}{2}\)
- C 1
- D \(\frac{\sin x}{(1+\sin x)^{2}}\)
Answer & Solution
Correct Answer
(B) \(-\frac{1}{2}\)
Step-by-step Solution
Detailed explanation
\(\frac{d}{d x}\left\{\tan ^{-1} \frac{\cos x}{1+\sin x}\right\}\) \(=\frac{1}{1+\left(\frac{\cos x}{1+\sin x}\right)^{2}} \frac{d}{d x} \frac{\cos x}{1+\sin x}\) \(=\frac{(1+\sin x)^{2}}{1+\sin ^{2} x+2 \sin x+\cos ^{2} x}\)…
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
- Aline cuts the \(x\) -axis at \(A(7,0)\) and the \(y\) -axis at \(B(0,-5)\). A variable line \(P Q\) is drawn perpendicular to \(A B\) cutting the \(x\) -axis at \(P(a, 0)\) and the \(y\) -axis at \(Q(0, b)\). If \(A Q\) and BP intersect at \(R\), the locus of \(R\) isWBJEE 2020 Hard
- If \(\sin ^{2} \theta+3 \cos \theta=2,\) then \(\cos ^{3} \theta+\sec ^{3} \theta\) is equal out toWBJEE 2013 Hard
- If the volume of the parallelopiped with \(\vec{a} \times \vec{b}, \vec{b} \times \vec{c}\) and \(\vec{c} \times \vec{a}\) as coterminous edges is 9 cu. units., then the volume of the parallelopiped with \((\vec{a} \times \vec{b}) \times(\vec{b} \times \vec{c}),(\vec{b} \times \vec{c}) \times(\vec{c} \times \vec{a})\) and \((\vec{c} \times \vec{a}) \times(\vec{a} \times \vec{b})\) as coterminous edges isWBJEE 2023 Medium
- The value of \(\lambda\) such that the system of equations \(2x-y-2 y=2 ; x-2 y+z=-4\),\(x+y+\lambda z=4,\) has no solution, isWBJEE 2015 Easy
- A relation \(\rho\) on the set of real number \(R\) is defined as \(\{x \rho y: x y>0\} .\) Then, which of the following is/are true?WBJEE 2015 Easy
- For the variable \(t,\) the locus of the points of intersection of lines \(x-2 y=t\) and \(x+2 y=\frac{1}{t}\) isWBJEE 2013 Medium
More PYQs from WBJEE
- \(A\) train is moving with a uniform speed \(c^{2}\) \(33 \mathrm{m} / \mathrm{s}\) and an observer is approaching the train with the same speed. If the train blows a whistle of frequency \(1000 \mathrm{Hz}\) and the velocity of sound is \(333 \mathrm{m} / \mathrm{s},\) then the apparent frequency of the sound that the observer hears isWBJEE 2015 Medium
- Let \(p, q\) be real numbers. If \(\alpha\) is the root of \(x^{2}+3 p^{2} x+5 q^{2}=0, \quad \beta \quad\) is \(\quad\) a \(\quad\) root \(\quad\) of \(x^{2}+9 p^{2} x+15 q^{2}=0\) and \(0 < \alpha < \beta,\) then the equation \(x^{2}+6 p^{2} x+10 q^{2}=0\) has a root \(\gamma\) that always satisfiesWBJEE 2014 Medium
- Electrons are emitted with kinetic energy \(T\) from a metal plate by an irradiation of light of intensity \(J\) and frequency v. Then, which of the following will be true?WBJEE 2019 Easy
- The equivalent capacitance of a combination of connected capacitors shown in the figure between the points P and N
is
WBJEE 2024 Easy - The number of real solutions of the equation \((\sin x-x)\left(\cos x-x^{2}\right)=0\) isWBJEE 2015 Medium
- In the following electron - dot structure, calculate the formal charge from left to right nitrogen atom; \(\ddot{\mathrm{N}}=\mathrm{N}=\ddot{\mathrm{N}}\)WBJEE 2011 Medium