Question:
The minimum value of f(x)=sin⁴x+cos⁴x in the interval (0,(π)/(2)) is:
The minimum value of f(x)=sin⁴x+cos⁴x in the interval (0,(π)/(2)) is:
Show Hint
Use symmetry of sine and cosine for extrema.
Updated On: Mar 18, 2026
- \frac12
- 2
- \sqrt2
- 1
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Verified By Collegedunia
The Correct Option is A
Solution and Explanation
Step 1: Use identity. sin⁴x+cos⁴x = (sin²x+cos²x)²-2sin²xcos²x
Step 2: Simplify. =1-2sin²xcos²x
Step 3: Minimum. Occurs at sin²x=cos²x=\frac12.
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