If $f(x)=\frac{\cos x}{\sin ^2 x+\cos ^4 x}$, for $x \in R$, then $f(2002)$ is equal to

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Aicharya · Accepted Answer

We have, $ f(x)=\frac{\cos ^2 x+\sin ^4 x}{\sin ^2 x+\cos ^4 x} $ $\begin{aligned} & =\frac{1-\sin ^2 x+\sin ^4 x}{1-\cos ^2 x+\cos ^4 x} \ & =\frac{1-\sin ^2 x\left(1-\sin ^2 xight)}{1-\cos ^2 x\left(1-\cos ^2 xight)} \ & =\frac{1-\sin ^2 x \cos ^2 x}{1-\cos ^2 x \sin ^2 x}=1 \ 	herefore \quad f(2002) & =1\end{aligned}$

If $f(x)=\frac{\cos x}{\sin ^2 x+\cos ^4 x}$, for $x \in R$, then $f(2002)$ is equal to

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