If A = sin2x + cos4x, then for all real x :

Engineering

Mathematics

Maximum and Minimum Value of Trigonometric Expression

Question

If A = sin²x + cos⁴x, then for all real x :

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\(\frac{3}{4} \le A \le \frac{{13}}{{16}}\)

\(\frac{3}{4} \le A \le 1\)

\(\frac{{13}}{{16}} \le A \le 1\)

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A = sin²x + cos⁴x

= sin²x + (1 – sin²x)²

= sin⁴x – sin²x + 1

\( = \left( {{{\sin }^2}x - \frac{1}{x}} \right) + \frac{3}{4}\)

\( = \frac{3}{4} \le A \le 1\)

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