KCET · Maths · Differentiation
If \( \cos y=x \cos (a+y) \) with \( \cos a \neq \pm 1 \), then \( \frac{d y}{d x} \) is equal to
- A \( \frac{\sin a}{\cos ^{2}(a+y)} \)
- B \( \frac{\cos ^{2}(a+y)}{\sin a} \)
- C \( \frac{\cos a}{\sin ^{2}(a+y)} \)
- D \( \frac{\cos ^{2}(a+y)}{\cos a} \)
Answer & Solution
Correct Answer
(B) \( \frac{\cos ^{2}(a+y)}{\sin a} \)
Step-by-step Solution
Detailed explanation
Given that \( \cos y=x \cos (a+y) \)
\[
\Rightarrow x=\frac{\cos y}{\cos (a+y)}
\]
Differentiating with respect to \( x \), we get
\[
\begin{array}{l}
1=\frac{(-\cos (a+y) \sin y+\sin (a+y) \cos y)}{\cos ^{2}(a+y)} \frac{d y}{d x} \\
\Rightarrow \frac{d y}{d x}=\frac{\cos ^{2}(a+y)}{\sin (a+y-y)}=\frac{\cos ^{2}(a+y)}{\sin a}
\end{array}
\]
\[
\Rightarrow x=\frac{\cos y}{\cos (a+y)}
\]
Differentiating with respect to \( x \), we get
\[
\begin{array}{l}
1=\frac{(-\cos (a+y) \sin y+\sin (a+y) \cos y)}{\cos ^{2}(a+y)} \frac{d y}{d x} \\
\Rightarrow \frac{d y}{d x}=\frac{\cos ^{2}(a+y)}{\sin (a+y-y)}=\frac{\cos ^{2}(a+y)}{\sin a}
\end{array}
\]
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 \(n\) is even and the middle term in the expansion of \(\left(x^2+\frac{1}{x}\right)^n\) is \(924 x^6\), then \(n\) is equal toKCET 2023 Easy
- If \(A\) and \(B\) are two independent events such that \(P(\bar{A})=0.75, P(A \cup B)=0.65\) and \(P(B)=x\), then find the value of \(x\).KCET 2022 Hard
- The mean deviation about the mean for the date \(4,7,8,9,10,12,13,17\) isKCET 2025 Medium
- If \(A = \{a, b, c, d, e, f\}\), then the number of subsets of A which contains at least \(2\) elements isKCET 2026 Easy
- A vector perpendicular to the plane containing the points \(A(1,-1,2), B(2,0,-1), C(0,2,1)\) isKCET 2007 Medium
- If \( \mathrm{A} \) is a matrix of order \( \mathrm{m} \times \mathrm{n} \) and \( \mathrm{B} \) is a matrix such that \( \mathrm{AB}^{\prime} \) and \( \mathrm{B}^{\prime} \mathrm{A} \) are both defined, the
order of the matrix \( B \) isKCET 2016 Medium
More PYQs from KCET
- In a typical heart, if EDV is 120 mL of blood and ESV is 50 mL of blood, the stroke volume (SV) isKCET 2011 Easy
- For sustained interference fringes in double slit experiment, essential condition/s is/are
1. sources must be coherent.
2. the intensities of the two sources must be equal.
Here, the correct option/s is/areKCET 2012 Easy - A mixture of \(\mathrm{CaCl}_{2}\) and \(\mathrm{NaCl}\) weighing \(4.44 \mathrm{~g}\) is treated with sodium carbonate solution to precipitate all the calcium ions as calcium carbonate. The calcium carbonate so obtained is heated strongly to get \(0.56 \mathrm{~g}\) of \(\mathrm{CaO}\). The percentage of \(\mathrm{NaCl}\) in the mixture is (atomic mass of \(\mathrm{Ca}=40\) )KCET 2011 Hard
- An electromagnetic wave is travelling in \( x \)-direction with electric field vector given by, \( \vec{E}_{y}=E_{0} \sin (k x-\omega t) \hat{j} \). The correct expression for magnetic field vector isKCET 2019 Easy
- A ray of light is incident on a surface of glass slab at an angle \(45^{\circ}\). If the lateral shift produced per unit thickness is \(\frac{1}{\sqrt{3}} \mathrm{~m}\), the angle of refraction produced isKCET 2009 Hard
- The function \(f(x)=[x]\), where \([x]\) denotes the greatest integer not greater than \(x\), isKCET 2010 Easy