MHT CET · Maths · Indefinite Integration
\(\int \frac{d x}{\cos 2 x-\cos ^{2} x}=\)
- A \(-\cot x+c\)
- B \(\tan x+c\)
- C \(-\tan x+c\)
- D \(\cot x+\mathrm{c}\)
Answer & Solution
Correct Answer
(D) \(\cot x+\mathrm{c}\)
Step-by-step Solution
Detailed explanation
(B)
\(\int \frac{d x}{\cos 2 x-\cos ^{2} x}=\int \frac{1}{2 \cos ^{2} x-1-\cos ^{2} x} d x=\int \frac{1}{\cos ^{2} x-1} d x\)
\(=\int \frac{-1}{1-\cos ^{2} x} d x=-\int \frac{d x}{\sin ^{2} x}=\int-\cos e c^{2} x d x=\cot x+c\)
\(\int \frac{d x}{\cos 2 x-\cos ^{2} x}=\int \frac{1}{2 \cos ^{2} x-1-\cos ^{2} x} d x=\int \frac{1}{\cos ^{2} x-1} d x\)
\(=\int \frac{-1}{1-\cos ^{2} x} d x=-\int \frac{d x}{\sin ^{2} x}=\int-\cos e c^{2} x d x=\cot x+c\)
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 \(\overline{\mathrm{b}}\) and \(\overline{\mathrm{c}}\) are unit vectors and \(|\bar{a}|=7\), \(\bar{a} \times(\bar{b} \times \bar{c})+\bar{b} \times(\bar{c} \times \bar{a})=\frac{1}{2} \bar{a}\), then angle between the vectors \(\bar{a}\) and \(\overline{\mathrm{c}}\) and angle between the vectors \(\overline{\mathrm{b}}\) and \(\overline{\mathrm{c}}\) are respectively.MHT CET 2025 Medium
- If \(y^2=a x^2+b x+c\), where \(a, b, c\) are constants, then \(y^3 \frac{d^2 y}{d x^2}\) is equal toMHT CET 2021 Easy
- The sum of focal radii of the curve \(90 x^{2}+25 y^{2}=225\) isMHT CET 2010 Easy
- The Cartesian equation of the line passing through the point \((-3,0,1)\) and perpendicular to vectors \(\hat{i}-2 \widehat{j}+\widehat{k}\) and \(2 \hat{i}+\widehat{j}-\widehat{k}\) isMHT CET 2022 Easy
- If \(\int \frac{\sin x}{\sin (x-\alpha)} d x=A x+B \log \sin (x-\alpha)+c\), then the value of \(\mathrm{A}\) and \(\mathrm{B}\) are respectively (where \(\mathrm{c}\) is a constant of integration)MHT CET 2021 Medium
- The joint equation of pair of lines through the origin and having slopes \((1+\sqrt{2})\) and \(\frac{1}{(1+\sqrt{2})}\) isMHT CET 2021 Medium
More PYQs from MHT CET
- When an ideal gas \(\left(\gamma=\frac{5}{3}\right)\) is heated under constant pressure, then what percentage of given heat energy will be utilised in doing external work?MHT CET 2025 Medium
- Select the incorrect statement about \(\mathrm{N}_2\) molecule.MHT CET 2025 Medium
- The conversion of 2- methylpropan – 1 – ol to 2- methylpropan -2- ol isMHT CET 2019 Easy
- In an interference experiment, third bright fringe is obtained at a point on the screen with a light of \(700 \mathrm{~nm}\). What should be the wavelength of the light source in order to obtain 5 th bright fringe at the same point?MHT CET 2009 Easy
- Which among the following is a multi-molecular colloid?MHT CET 2021 Easy
- What is the number of unpaired electrons in \(\left[\mathrm{Co}\left(\mathrm{NH}_3\right)_6\right]^{+3}\) complex?MHT CET 2022 Easy