Question:medium

If $f(x) = sin^{6}x + cos^{6}x$ then the range of $f(x)$ is

Show Hint

$sin^{4}x + cos^{4}x = 1 - \frac{1}{2}sin^{2}2x$ and $sin^{6}x + cos^{6}x = 1 - \frac{3}{4}sin^{2}2x$.

Updated On: Jul 4, 2026

$(1/4, 3/4)$
$[1/4, 1]$
$[1/4, 3/4]$
$[3/4, 1]$

Show Solution

The Correct Option is B

Solution and Explanation

Was this answer helpful?

0

Top Questions on Trigonometry

If \( \tan^{-1}\left(\frac{1}{1+1\cdot2}\right) + \tan^{-1}\left(\frac{1}{1+2\cdot3}\right) + \ldots + \tan^{-1}\left(\frac{1}{1+n(n+1)}\right) = \tan^{-1}(x) \), then \( x \) is equal to:
- BITSAT - 2024
- Mathematics
- Trigonometry
View Solution
If \[ y = \tan^{-1} \left( \frac{1}{x^2 + x + 1} \right) + \tan^{-1} \left( \frac{1}{x^2 + 3x + 3} \right) + \tan^{-1} \left( \frac{1}{x^2 + 5x + 7} \right) + \cdots { (to n terms)} \], then \(\frac{dy}{dx}\) is:
- BITSAT - 2024
- Mathematics
- Trigonometry
View Solution
Let \(A\), \(B\) and \(C\) are the angles of a triangle and \(\tan \frac{A}{2} = 1/3\), \(\tan \frac{B}{2} = \frac{2}{3}\). Then, \(\tan \frac{C}{2}\) is equal to:
- BITSAT - 2024
- Mathematics
- Trigonometry
View Solution
The sum of all values of \(x\) in \([0, 2\pi]\), for which \(x + \sin(2x) + \sin(3x) + \sin(4x) = 0\) is equal to:
- BITSAT - 2024
- Mathematics
- Trigonometry
View Solution
Want to practice more? Try solving extra ecology questions todayView All Questions

Questions Asked in AP ECET Metallurgical Eng exam

Order of the matrix $\begin{bmatrix} 1 & 6 \\ 2 & 0 \\ 7 & -1 \end{bmatrix}$ is

If two rows (or columns) of a determinant of order 3 are identical then the value of determinant is

Co-factor of -4 in $\begin{vmatrix} 1 & 2 & 3 \\ -4 & 3 & 6 \\ 2 & -7 & 9 \end{vmatrix}$ is

The Matrix $\begin{bmatrix} a & h & g \\ h & b & f \\ g & f & c \end{bmatrix}$ is