AP EAMCET · Maths · Trigonometric Equations
If \(f_n(x)=\frac{1}{2 n}\left[\sin ^{2 n} x+\cos ^{2 n} x\right]\), then \(f_1(x)+f_2(x)-f_3\) (x) \(=\)
- A 0
- B \(\frac{5}{12}\)
- C \(\frac{11}{12}\)
- D \(\frac{7}{12}\)
Answer & Solution
Correct Answer
(D) \(\frac{7}{12}\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & \text {} f_n(x)=\frac{1}{2 n}\left[\sin ^{2 n} x+\cos ^{2 n} x\right] \\ & f_1(x)+f_2(x)+f_3(x) \\ & =\frac{1}{2}\left[\sin ^2 x+\cos ^2 x\right]+\frac{1}{4}\left[\sin ^4 x+\cos ^4 x\right]-\frac{1}{6}\left[\sin ^6 x+\cos ^6 x\right] \\ & =\frac{1}{2} \times…
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 mean marks of 25 boys in a class is 61 and the mean marks of 35 girls in the same class is 58 . Then, the mean of all 60 students isAP EAMCET 2021 Medium
- \(f(x)\) is a quadratic polynomial satisfying the condition \(f(x)+f\left(\frac{1}{x}\right)=f(x) f\left(\frac{1}{x}\right)\). If \(f(-1)=0\), then the range of \(f\) isAP EAMCET 2025 Medium
- If \(\frac{1+3 P}{3}, \frac{1-2 P}{2}\) are probabilities of two mutually exclusive events, then \(P\) lies in the interval.AP EAMCET 2015 Easy
- If \(\mathbf{O A}=2 \hat{\mathbf{i}}+2 \hat{\mathbf{j}}+\hat{\mathbf{k}}, \mathbf{O B}=2 \hat{\mathbf{i}}+4 \hat{\mathbf{j}}+4 \hat{\mathbf{k}}\) and the length of the internal bisector of \(\angle B O A\) of triangle \(A O B\) is \(k\), then \(9 k^2=\)AP EAMCET 2019 Easy
- If \(\frac{x+1}{(2 x-1)(3 x+1)}=\frac{A}{2 x-1}+\frac{B}{3 x+1}\), then \(16 A+9 B\) is equal toAP EAMCET 2020 Easy
- Suppose \(A\) and \(B\) are the points at which the line \(x+y-\lambda=0\) meets the pair of straight lines \(x^2+y^2-2 x-4 y+2=0\). If \(\angle A O B=90^{\circ}\), then a value of \(\lambda\) isAP EAMCET 2022 Medium
More PYQs from AP EAMCET
- The amplitudes of a damped harmonic oscillator after 2 and 4 seconds are \(A_1\) and \(A_2\) respectively. If the initial amplitude of the oscillator is \(\mathrm{A}_0\), thenAP EAMCET 2023 Hard
- If \(f: \mathbb{R}-\{0\} \rightarrow \mathbb{R}\) is defined by \(f(x)=x+\frac{1}{x}\) and if \(f^k(x)=[f(x)]^k\) for \(k \geq 1\) then \(f^4(x)-f\left(x^4\right)-4 f^2(x)=\)AP EAMCET 2017 Medium
- Identify the amino acid which has
AP EAMCET 2024 Medium - A block of mass ' \(\mathrm{m}\) ' and charge ' \(\mathrm{q}\) ' is connected to a point ' \(O\) ' with an inextensible string. This system is on a horizontal table. An electric field (E) is applied perpendicular to the string and in the plane of the horizontal table. The tension in the string when it becomes parallel to the electric field isAP EAMCET 2023 Hard
- Two point charges \(+6 \mu \mathrm{C}\) and \(+10 \mu \mathrm{C}\) kept at certain distance repel each other with a force of 30 N . If each charge is given an additional charge of \(-8 \mu \mathrm{C}\), the two chargesAP EAMCET 2024 Easy
- If \(x\) is numerically so small so that \(x^2\) and higher powers of \(x\) can be neglected, then \(\left(1+\frac{2 x}{3}\right)^{3 / 2} \cdot(32+5 x)^{-1 / 5}\) is approximately equal toAP EAMCET 2009 Easy