QJEEM19Ma1287: JEE Main 2019 Mathematics - Class 11 JEEM19Ma1287 Solution: Let f k (x) = 1 k ( sin k x + cos k x ) for k = 1, 2, 3, ...…

Question

Verified Solution • 2025–26 Session moderate

Let f_k(x) =

\frac{1}{k} (\sin^{k} x + \cos^{k} x)

for k = 1, 2, 3, ... Then for all x

\in

R, the value of f₄(x)

-

f₆(x) is equal to

Accepted Answer

f₄(x)

-

f₆(x)

=

\frac{1}{4}

(sin⁴ x + cos⁴ x)

-

\frac{1}{6}

(sin⁶ x + cos⁶ x)

=

\frac{1}{4}

(1

-

\frac{1}{2}

sin² 2x)

-

\frac{1}{6}

(1

-

\frac{3}{4}

sin² 2x) =

\frac{1}{12}

Step-by-Step Verified Solution