Question

smallest value of, (sin²A+cos⁴A)
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Answer 1

Answer:

A is = 3/4

Step-by-step explanation:

By trigonometric identity, sin²A = 1 - cos²A

ii) Hence, cos⁴A + sin²A = cos⁴A - cos²A + 1 = cos⁴A - cos²A + 1/4 + 3/4

= (cos²A - 1/2)² + 3/4

iii) For all A real, (cos²A - 1/2)² ≥ 0 and ≤ 1/4 {Since cos value lies in [-1, 1] only}

So minimum value of (cos²A - 1/2)² = 0

So minimum value of (cos²A - 1/2)² + 3/4 = 3/4

Thus minimum value of cos⁴A + sin²A for all real A is = 3/4

Answer 2

Step-by-step explanation:

answer is 3/4

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