AP EAMCET · Maths · Differentiation
If \(\frac{y}{x} \cos ^4 \alpha+\frac{x}{y} \sin ^4 \alpha=2 \sin ^2 \alpha \cdot \cos ^2 \alpha\), then \(\frac{d y}{d x}=\)
- A \(\sin ^3 \alpha \cos \alpha\)
- B \(\sin ^2 \alpha \cos ^2 \alpha\)
- C \(\frac{\sin ^2 \alpha}{\cos ^2 \alpha}\)
- D \(\sin \alpha \cos ^3 \alpha\)
Answer & Solution
Correct Answer
(C) \(\frac{\sin ^2 \alpha}{\cos ^2 \alpha}\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & \text { we have } \frac{\mathrm{y}}{\mathrm{x}} \cos ^4 \alpha+\frac{\mathrm{x}}{\mathrm{y}} \sin ^4 \alpha=2 \sin ^2 \alpha \cdot \cos ^2 \alpha \\ & \Rightarrow \mathrm{x}^2 \sin ^4 \alpha+\mathrm{y}^2 \cos ^4 \alpha-2 \mathrm{xy} \sin ^2 \alpha \cos ^2…
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 the foot of the perpendicular from \((0,0,0)\) to a plane is \((1,2,3)\), then the equation of the plane isAP EAMCET 2012 Medium
- If \(1-\cot 23^{\circ}=\frac{x}{1-\cot 22^{\circ}}\), then \(x=\)AP EAMCET 2022 Medium
- If \(A+2 B=\left(\begin{array}{ccc}1 & 2 & 0 \\ 6 & -3 & 3 \\ -5 & 3 & 1\end{array}\right)\) and \(2 A-B=\left(\begin{array}{ccc}2 & -1 & 5 \\ 2 & -1 & 6 \\ 0 & 1 & 2\end{array}\right)\) then \(\operatorname{Tr}[\mathrm{A}]-\operatorname{Tr}[\mathrm{B}]=\)AP EAMCET 2023 Easy
- If \(x=-\frac{1}{2}, \sinh ^{-1} x+\operatorname{cosech}^{-1} x=\)AP EAMCET 2018 Medium
- \(g(x)\) is an anti derivative of \(f(x)=1+2^x \log 2\) and the graph of \(y=g(x)\) passes through \(\left(-1, \frac{1}{2}\right)\). Then the curve meets the \(\mathrm{Y}\) - axis atAP EAMCET 2023 Easy
- A unit vector that is perpendicular to the vector \(2 \overline{\mathrm{i}}-\overline{\mathrm{j}}+2 \overline{\mathrm{k}}\) and coplanar with the vectors \(\overline{\mathrm{i}}+\overline{\mathrm{j}}-\overline{\mathrm{k}}\) and \(2 \overline{\mathrm{i}}+2 \overline{\mathrm{j}}-\overline{\mathrm{k}}\) isAP EAMCET 2025 Medium
More PYQs from AP EAMCET
- Two waves of frequency \(f\) and amplitude \(a\) superimpose with each other. The total intensity is directly proportional toAP EAMCET 2020 Easy
- \(S_1, S_2, \ldots \ldots, S_{10}\) are the speakers in a conference. If \(S_1\) addresses only after \(S_2\), then the number of ways the speakers address isAP EAMCET 2004 Medium
- If a proton is accelerated to a velocity of \(3 \times 10^7 \mathrm{~ms}^{-1}\) which is accurate up to \(\pm 0.5 \%\), then the uncertainty in its position will be \(\ldots \ldots \ldots\) [mass of proton \(=1.66 \times 10^{-27} \mathrm{~kg}\), \(\left.h=6.6 \times 10^{-34} \mathrm{Js}\right]\)AP EAMCET 2021 Medium
- In a \(\triangle \mathrm{ABC}\) if \(a=26, b=30, \cos C=\frac{63}{65}\) then \(C=\)AP EAMCET 2024 Medium
- Heat energy absorbed by a system going through the cyclic process shown in the figure is
AP EAMCET 2024 Easy - The solution of the differential equation \(e^x y d x+e^x d y+x d x=0\) isAP EAMCET 2024 Easy