AP EAMCET · Maths · Functions
The maximum and minimum values of the function \(f:[R \rightarrow[R\) defined by \(f(x)=5 \cos x+3 \cos \left(x+\frac{\pi}{3}\right)+8\) for all \(x \in[R\), are respectively.
- A 15, 1
- B 8, - 8
- C -7, - 15
- D 1, - 15
Answer & Solution
Correct Answer
(A) 15, 1
Step-by-step Solution
Detailed explanation
\begin{aligned} & f(x)=5 \cos x+3 \cos \left(x+\frac{\pi}{3}\right)+8 \\ & =5 \cos x+3\left[\cos x \cdot \cos \frac{\pi}{3}-\sin x \sin \frac{\pi}{3}\right]+8 \\ & =5 \cos x+3\left[\frac{1}{2} \cos x-\frac{\sqrt{3}}{2} \sin x\right]+8 \\ & =\frac{13}{2} \cos x-\frac{3…
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 value of \(\int \frac{e^{\tan ^{-1}(x)}}{1+x^2}\) \(\left[\left(\sec ^{-1} \sqrt{1+x^2}\right)^2+\cos ^{-1}\left(\frac{1-x^2}{1+x^2}\right)\right] d x\), for \(x>0\) isAP EAMCET 2021 Hard
- If \(A=\left[\begin{array}{ccc}-1 & x & -3 \\ 2 & 4 & z \\ y & 5 & -6\end{array}\right]\) is a symmetric matrix and \(B=\left[\begin{array}{ccc}0 & 2 & q \\ p & 0 & -4 \\ -3 & r & s\end{array}\right]\) is a skew symmetric matrix, then \(|A|+|B|-|A B|=\)AP EAMCET 2025 Medium
- For \(A, B\) and \(C\), if \(A+B+C=0\), then \(\sin (2 A)+\sin (2 B)+\sin (2 C)\) is equal toAP EAMCET 2020 Easy
- Tangents are drawn to the hyperbola \(x^2-9 y^2=9\) from point \((3,2)\). Then, the area of the triangle formed by the tangents and the chord of contact is ____ sq units.AP EAMCET 2020 Medium
- If \(\int \frac{\log \left(1+x^4\right)}{x^3} d x=f(x) \log \left(\frac{1}{g(x)}\right)+\tan ^{-1}(h(x))+c\), then \(h(x)\left[f(x)+f\left(\frac{1}{x}\right)\right]=\)AP EAMCET 2024 Hard
- If the mean and standard deviation of a binomial distribution are and , respectively, then the number of trials is ________AP EAMCET 2020 Easy
More PYQs from AP EAMCET
- If the vectors \(a \hat{i}+\hat{j}+\hat{k} ; \hat{i}+b \hat{j}+\hat{k} ; \hat{i}+\hat{j}+c \hat{k}(\mathrm{a} \neq \mathrm{b} \neq \mathrm{c} \neq 1)\) are coplanar then \(\frac{1}{1-a}+\frac{1}{1-b}+\frac{1}{1-c}=\)AP EAMCET 2024 Medium
- The sum of electrons present in all sub shells of an atom with \(m_s\) value of \(+\frac{1}{2}\) for \(n=4\) and \(m_s\) value of \(-\frac{1}{2}\) for \(\mathrm{n}=3\) isAP EAMCET 2022 Easy
- \(4 \mathrm{~g}\) of a hydrocarbon on complete combustion gave \(12.571 \mathrm{~g}\) of \(\mathrm{CO}_2\) and \(5.143 \mathrm{~g}\) of water. What is the empirical formula of the hydrocarbon?AP EAMCET 2002 Medium
- AP EAMCET 2022 Hard
- If the normal to the curve \(y=x+\frac{2}{x}\) at the point where abscissa is 2 , meets the coordinate axes in points \(A \& B\), find the length of \(A B\).AP EAMCET 2020 Easy
- If the axes are transformed to the point (− 1,1), then the equation
\(3 x^2+y^2+2 x+4 y+15=0\) would transformAP EAMCET 2021 Medium