AP EAMCET · Maths · Application of Derivatives
The number of all the values of \(x\) for which the function \(f(x)=\sin x+\frac{1-\tan ^2 x}{1+\tan ^2 x}\) attains its maximum value on \([0,2 \pi]\) is
- A 4
- B 1
- C 2
- D infinite
Answer & Solution
Correct Answer
(C) 2
Step-by-step Solution
Detailed explanation
\begin{aligned} & \text { } f(x)=\sin x+\frac{1-\tan ^2 x}{1+\tan ^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…
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