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

Question

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 (A) 1 (B) 3 (C) (7/4) (D) 5

Tardigrade Admin · Accepted Answer

f ( x )=3-(5/4) sin 2(2 x ) ≤ 3 ∀ x ∈ R ∴ f max =3

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