AP EAMCET · Maths · Functions
If \(2 f(\sin x)+f(\cos x)=x\), then \(f^{\prime}(x)=\)
- A \(\frac{1}{\sqrt{1-x^2}}\)
- B \(\frac{-1}{\sqrt{1-x^2}}\)
- C \(\frac{x}{\sqrt{1-x^2}}\)
- D \(\frac{-x}{\sqrt{1-x^2}}\)
Answer & Solution
Correct Answer
(A) \(\frac{1}{\sqrt{1-x^2}}\)
Step-by-step Solution
Detailed explanation
It is given that, \(2 f(\sin x)+f(\cos x)=x\) ...(i) by replacing \(x\) by \(\frac{\pi}{2}-x\), we get \(2 f(\cos x)+f(\sin x)=\frac{\pi}{2}-x\) ...(ii) from Eqs. (i) and (ii), we get \(3 f(\sin x)=3 x-\frac{\pi}{2}\)…
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