Question:medium
The minimum value of \( \sin x + \cos x \) is:
The minimum value of \( \sin x + \cos x \) is:
Show Hint
Another useful form is
\[
\sin x+\cos x=\sqrt{2}\sin\left(x+\frac{\pi}{4}\right)
\]
Since the minimum value of sine is \(-1\), the minimum value becomes \(-\sqrt{2}\).
Updated On: May 6, 2026
- \( \sqrt{2} \)
- \( -\sqrt{2} \)
- \( \frac{1}{\sqrt{2}} \)
- \( -\frac{1}{\sqrt{2}} \)
- \( 1 \)
Show Solution
The Correct Option is B
Solution and Explanation
Was this answer helpful?
0
Top Questions on Maxima and Minima
Define \( f(x) = \begin{cases} x^2 + bx + c, & x< 1 \\ x, & x \geq 1 \end{cases} \). If f(x) is differentiable at x=1, then b−c is equal to
- MHT CET - 2024
- Mathematics
- Maxima and Minima
- The maximum value of the function \( f(x) = -2x^2 + 4x + 1 \) occurs at:
- MHT CET - 2025
- Mathematics
- Maxima and Minima
- Let $ f(x) = |x^2 - 4x + 3| + |x^2 - 5x + 6| $. The minimum value of $ f(x) $ is:
- BITSAT - 2025
- Mathematics
- Maxima and Minima
- Determine the number of units (\( x \)) that should be sold to maximise the revenue \( R(x) = x \cdot p(x) \). Also verify the result.
- CBSE Class XII - 2024
- Mathematics
- Maxima and Minima
- Want to practice more? Try solving extra ecology questions todayView All Questions
