TS EAMCET · Maths · Indefinite Integration
If \(\int(1-\cos x) \operatorname{cosec}^2 x d x=f(x)+c\), then \(f(x)\) is equal to
- A \(\tan \frac{x}{2}\)
- B \(\cot \frac{x}{2}\)
- C \(2 \tan \frac{x}{2}\)
- D \(\frac{1}{2} \tan \frac{x}{2}\)
Answer & Solution
Correct Answer
(A) \(\tan \frac{x}{2}\)
Step-by-step Solution
Detailed explanation
\(\int(1-\cos x) \operatorname{cosec}^2 x d x\) \(=\int\left(2 \sin ^2 \frac{x}{2}\right) \cdot \frac{1}{\sin ^2 x} d x\) \(\left[\because \cos x=1-2 \sin ^2 \frac{x}{2}\right]\) \(=2 \int \frac{\sin ^2 \frac{x}{2}}{\left(2 \sin \frac{x}{2} \cdot \cos \frac{x}{2}\right)^2} d x\)…
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
- The area (in sq units) bounded by the curves \(y^2=4 x\) and \(x^2=4 y\) isTS EAMCET 2012 Easy
- A five digit number is formed by the digits 1 , \(2,3,4,5\) with no digit being repeated. The probability that the number is divisible by 4 , isTS EAMCET 2016 Easy
- Let \(l_1\) and \(l_2\) be two lines intersecting at \(P\). If \(A_1, B_1, C_1\) are points on \(l_1\), and \(A_2, B_2, C_2, D_2, E_2\) are points on \(l_2\) and if none of these coincides with \(P\), then the number of triangles formed by these eight points, is :TS EAMCET 2003 Medium
- If \(\int \frac{(x-1) d x}{(x+1) \sqrt{x^3+x^2+x}}=A \cdot \tan ^{-1} \sqrt{f(x)}+\) constant, then the ordered pair \((A, f(-1))=\)TS EAMCET 2020 Hard
- Statement (I) : The range of the ungrouped data does not change even if certain intermediate observations are removed. Statement (II) : The value of the mean deviation of an ungrouped data about the median is always less than or equal to the value of the mean deviation computed about any other measure of central tendency. Statement (III) : For a grouped data, range is approximated as the difference between the lower limit of the largest class and the upper limit of the smallest class.TS EAMCET 2022 Medium
- In a test, a student either guesses or copies or knows the answer to a multiple choice question with four choices having one correct answer. The probability that he guesses the answer is \(\frac{1}{3}\) and the probability that he copies it is \(\frac{1}{12}\). The probability that his answer is correct given that he copied it is \(\frac{1}{6}\). The probability that he knew the answer, given that he has correctly answered it, isTS EAMCET 2018 Hard
More PYQs from TS EAMCET
- A steam at \(100^{\circ} \mathrm{C}\) is passed into \(1 \mathrm{~kg}\) of water contained in a calorimeter of water equivalent \(0.2 \mathrm{~kg}\) at \(9^{\circ} \mathrm{C}\) till the temperature of the calorimeter and water in it is increased to \(90^{\circ} \mathrm{C}\). The mass of steam condensed in \(\mathrm{kg}\) is nearly (specific heat of water \(=1 \mathrm{cal} / \mathrm{g}{ }^{\circ} \mathrm{C}\), latent heat of vaporisation \(=540 \mathrm{cal} / \mathrm{g}\) )TS EAMCET 2014 Medium
- Let \(S\) be the sample space of the random experiment of throwing simultaneously two unbiased dice with six faces (numbered 1 to 6 ) and let \(E_k=\{(a, b) \in S: a b=k\}\) for \(k \geq 1\). If \(p_k+P\left(E_k\right)\) for \(k \geq 1\), then the correct among the following, isTS EAMCET 2008 Medium
- \(\vec{b}=\hat{i}-\hat{j}+2 \hat{k}, \vec{c}=\hat{i}+2 \hat{j}-\hat{k}\) are two vectors and \(\vec{a}\) is a vector such that \(\cos (\vec{a}, \vec{b} \times \vec{c})=\sqrt{\frac{2}{3}}\). If \(\vec{a}\) is a unit vector, then \(|\vec{a} \times(\vec{b} \times \vec{c})|=\)TS EAMCET 2024 Hard
- A solid sphere of radius makes a perfect rolling down on a plane which is inclined to the horizontal axis at an angle . If the radius of gyration is , then its acceleration isTS EAMCET 2018 Hard
- Which of the following is an endothermic reaction?TS EAMCET 2004 Easy
- A body centred cubic lattice is made up of two different types of atoms X and Y. Atom X occupies the body centre and atoms \(\mathrm{Y}\) occupy the corner positions. One of the corners is left unoccupied per unit cell. The empirical formula of it isTS EAMCET 2023 Medium