If-A-sin-4-cos-4-then-select-the-correct-option-i-0-lt-A-lt-1-2-ii-1-lt-A-lt-3-2-iii-1-2-A-1-iv-3-2-A-2-

Question Number 206618 by MATHEMATICSAM last updated on 20/Apr/24

If A = \sin^{4} θ + \cos^{4} θ then select the

correct option :

i) 0 < A < \frac{1}{2}

ii) 1 < A < \frac{3}{2}

iii) \frac{1}{2} \leq A \leq 1

iv) \frac{3}{2} \leq A \leq 2

Answered by MM42 last updated on 20/Apr/24

A = {({s i n}^{2} θ + {c o s}^{2} θ)}^{2} - 2 {s i n}^{2} θ {c o s}^{2} θ

= 1 - \frac{1}{2} {s i n}^{2} (2 θ) \Rightarrow a n s : \frac{1}{2} ⩽ A ⩽ 1 ✓

Answered by Frix last updated on 20/Apr/24

A = \frac{3}{4} + \frac{\cos 4 x}{4}

\frac{1}{2} ⩽ A ⩽ 1

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