AP EAMCET · Maths · Application of Derivatives
The minimum value of \(\left(1+\frac{1}{\sin ^n \alpha}\right)\left(1+\frac{1}{\cos ^n \alpha}\right)\) is
- A \(1\)
- B \(2\)
- C \(\left(1+2^n\right)^2\)
- D \(\left(1+2^{n / 2}\right)^2\)
Answer & Solution
Correct Answer
(D) \(\left(1+2^{n / 2}\right)^2\)
Step-by-step Solution
Detailed explanation
Let \(f(x)=\left(1+\frac{1}{\sin ^n x}\right)\left(1+\frac{1}{\cos ^n x}\right)\) \(=\left(1+\operatorname{cosec}^n x\right)\left(1+\sec ^n x\right)\)…
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 probability function of a random variable \(X\) is given by \(P(X=k)=c k^2\), where \(c\) is a constant and \(k \in\{0,1,2,3,4\}\). If \(\sigma^2\) is the variance of \(X\) and \(\mu\) is the mean of \(X\), then \(\sigma^2+\mu^2=\)AP EAMCET 2019 Medium
- If \(\alpha\) is a common root of \(x^2-5 x+\lambda=0\) and \(x^2-8 x-2 \lambda\) \(=0(\lambda \neq 0)\) and \(\beta, \gamma\) are the other roots of them, then \(\alpha+\beta+\gamma+\lambda=\)AP EAMCET 2024 Easy
- If \(\alpha\) and \(\beta\) are two distinct negative roots of \(x^5-5 x^3+5 x^2-1=0\), then the equation of least degree with integer coefficients having \(\sqrt{-\alpha}\) and \(\sqrt{-\beta}\) as its roots isAP EAMCET 2024 Medium
- Define \(f(x)=\left\{\begin{array}{cc}x^2+b x+c, & x < 1 \\ x, & x \geq 1\end{array}\right.\). If \(f(x)\) is differentiable at \(x=1\), then \((b-c)\) is equal toAP EAMCET 2016 Medium
- The equation of the circle which cuts the circles \(x^2+y^2+4 x-7=0\), \(2 x^2+2 y^2+3 x+5 y-9=0, x^2+y^2+y=0\) orthogonally isAP EAMCET 2019 Medium
- Let \(f(x)\) be a real valued function. If \(f^{\prime}(x)\) is a constant for all \(x \in \mathbb{R}, f(0)=2\) and \(f^{\prime}(0)=1\), thenAP EAMCET 2023 Medium
More PYQs from AP EAMCET
- In the given reactions, ' \(\mathrm{X}\) ' and ' \(\mathrm{Y}\) ' respectively are
\(\mathrm{C}_6 \mathrm{H}_5 \mathrm{CH}_2 \mathrm{NH}_2 \stackrel{\mathrm{X}}{\longleftrightarrow} \mathrm{C}_6 \mathrm{H}_5 \mathrm{CONH}_2 \stackrel{\mathrm{Y}}{\longrightarrow} \mathrm{C}_6 \mathrm{H}_5 \mathrm{NH}_2\)AP EAMCET 2023 Medium - If \((3+\sqrt{2})^6-(3-\sqrt{2})^6=a+b \sqrt{2}\), then \(a+b=\)AP EAMCET 2023 Easy
- \(3.1 \mathrm{~g}\) of a compound, ' \(X\) ' (molar mass \(=62 \mathrm{~g}\) \(\mathrm{mol}^{-1}\) ) is dissolved in \(19.5 \mathrm{~g}\) of other compound, \(Y\) (molar mass \(=78 \mathrm{~g} \mathrm{~mol}^{-1}\) ). The ratio of mole fractions of \(X\) and \(Y\) in the solution isAP EAMCET 2022 Medium
- What is the molecular formula of the product formed when benzene is reacted with ethyl chloride in presence of anhydrous aluminium chloride?AP EAMCET 2004 Medium
- Define \(f: \mathbb{R} \rightarrow \mathbb{R}\) by \(f(x)=[x]+\sqrt{x-[x]}\) for \(x \in \mathbb{R}\), where \([x]\) denotes the greatest integer function. Then the set of points at which \(f\) is continuous isAP EAMCET 2017 Medium
- A car moving with a velocity \(6.25 \mathrm{~ms}^{-1}\) is decelerated with \(2.5 \sqrt{\mathrm{v}} \mathrm{ms}^{-2}\) ( \(v\) is instantaneous velocity). Time taken by the car to come to rest isAP EAMCET 2019 Easy