The number of all the values of $x$ for which the function $f(x)=\sin x+\frac{1- an ^2 x}{1+ an ^2 x}$ attains its maximum value on $[0,2 \pi]$ is

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The number of all the values of $x$ for which the function $f(x)=\sin x+\frac{1-	an ^2 x}{1+	an ^2 x}$ attains its maximum value on $[0,2 \pi]$ is

Aicharya · Accepted Answer

$\begin{aligned} & 	ext { } f(x)=\sin x+\frac{1-	an ^2 x}{1+	an ^2 x} \Rightarrow f(x)=\sin x+\cos 2 x \ & f^{\prime}(x)=\cos x-2 \sin 2 x=0 \Rightarrow \cos x=2 \sin 2 x \ & \Rightarrow 1=2 \sin x \Rightarrow \sin x=\sin \frac{\pi}{6} \Rightarrow x=n \pi+(-1)^n \frac{\pi}{6} \end{aligned}$ $	herefore$ Only two values are possible in $[0,2 \pi]$ which are $\frac{\pi}{6}, \frac{5 \pi}{6}$

The number of all the values of $x$ for which the function $f(x)=\sin x+\frac{1-\tan ^2 x}{1+\tan ^2 x}$…

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