If f (x )= cos^2 ⁡x+ sin^4 ⁡x sin^2 ⁡x+ cos^4 ⁡x ∀x ∈R, then f (2023 )=

Question

Accepted Answer

Correct answer: A. (a) ∵f (x )= cos^2 ⁡x+ sin^4 ⁡x sin^2 ⁡x+ cos^4 ⁡x = cos^2 ⁡x+ sin^2 ⁡x- sin^2 ⁡x+ sin^4 ⁡x sin^2 ⁡x+ cos^2 ⁡x- cos^2 ⁡x+ cos^4 ⁡x = 1- sin^2 ⁡x(1- sin^2 ⁡x)1- cos^2 ⁡x (1 cos^2 ⁡x ) ⇒f (x )= 1- sin^2 ⁡x cos^2 ⁡x1- cos^2 ⁡x sin^2 ⁡x=1 ⇒f (x )=1 ⇒f (2023 )=1

$If f (x) = \frac{cos ^{2} x + sin ^{4} x}{sin ^{2} x + cos ^{4} x} \forall x \in R, then f (2023) =$

Solution

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