Let f k (x) = 1/k(sin ^(k)x + cos ^(k)x) where x R and k ≥ 1. Then f₄(x) - f₆(x) equals:

Trigonometry: JEE Main 2014 Mathematics question

JEE Main 2014 · Session, Shift 1 · Q5644

JEE Main 2014Session, Shift 1MathematicsMediumTrigonometry118× since 2002

Let

f_k\left( x \right) = {1 \over k}\left( {{{\sin }^k}x + {{\cos }^k}x} \right)

where

x \in R

and

k \ge \,1.

Then

{f_4}\left( x \right) - {f_6}\left( x \right)\,\,

equals :

JEE Main 2014 · Session, Shift 1 · Q5644

JEE Main 2014Session, Shift 1MathematicsMediumTrigonometry118× since 2002

Let

f_k\left( x \right) = {1 \over k}\left( {{{\sin }^k}x + {{\cos }^k}x} \right)

where

x \in R

and

k \ge \,1.

Then

{f_4}\left( x \right) - {f_6}\left( x \right)\,\,

equals :