Let … where … and … Then … equals :

Trigonometric Ratio and Identites

JEE Main 2014 · Session, Shift 1 · Q5644

MathematicsMedium45×since 2004Q5644

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

MathematicsMedium45×since 2004Q5644

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 :