JEE Main 2014 · 6 Apr · Shift 1 · Mathematics Q88

MathematicsSingle correct+4 / -1Question 88 of 90

Let $f_k(x)=\dfrac1k\left(\sin^kx+\cos^kx\right)$ where $x\in\mathbf R$ and $k\ge1$ . Then $f_4(x)-f_6(x)$ equals :

\dfrac14

\dfrac1{12}

\dfrac16

\dfrac13

Answer and worked solution

Official answer: B

With $u=\sin^2x\cos^2x$ : $\sin^4x+\cos^4x=1-2u$ and $\sin^6x+\cos^6x=1-3u$ . So
$f_4-f_6=\frac{1-2u}4-\frac{1-3u}6=\frac1{12}.$

JEE Main 2014 · 6 Apr · Shift 1, Mathematics question 88