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  4. The greatest value of the function f(x)= displaystyle∑n=13(( sin 2 x)n+( cos 2 x)n) for all x ∈ R is equal to

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Q. The greatest value of the function $f(x)=\displaystyle\sum_{n=1}^3\left(\left(\sin ^2 x\right)^n+\left(\cos ^2 x\right)^n\right)$ for all $x \in R$ is equal to

Relations and Functions - Part 2

Solution:

$f ( x )=3-\frac{5}{4} \sin ^2(2 x ) \leq 3 \forall x \in R$
$\therefore f _{\max }=3 $